Exercise algebra.manipulation.exponents.nonnegative

Description
write with a non-negative exponent

Derivations

1.

a*b^(-2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

a/b^2

2.

a^(-1)*b^2

⇒ algebra.manipulation.exponents.reciprocal-inverse

b^2/a

3.

a^(-2)*b^(-3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

b^(-3)/a^2

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(b^3*a^2)

4.

1/a^(-3)*(b^(-2))^2

⇒ algebra.manipulation.exponents.mul-exponents

b^(-4)/a^(-3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(b^4*a^(-3))

⇒ algebra.manipulation.exponents.reciprocal-inverse

a^3/b^4

5.

1/(a*b)^(-2)*a*b^(-1)

⇒ algebra.manipulation.exponents.reciprocal-inverse

(a*b)^2*a*b^(-1)

⇒ algebra.manipulation.exponents.reciprocal-inverse

(a*b)^2*a/b

⇒ algebra.manipulation.exponents.distr-power

a^2*b^2*a/b

⇒ algebra.manipulation.exponents.add-exponents

a^3*b^2/b

⇒ algebra.manipulation.exponents.sub-exponents

a^3*b

6.

(2*a)^(-1)/(4*b)^(-2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(2*a*(4*b)^(-2))

⇒ algebra.manipulation.exponents.reciprocal-inverse

(4*b)^2/(2*a)

⇒ algebra.manipulation.exponents.distr-power

8*b^2/a

7.

(4*a*b)^(-1)*(b^2)^(-3)

⇒ algebra.manipulation.exponents.mul-exponents

(4*a*b)^(-1)*b^(-6)

⇒ algebra.manipulation.exponents.reciprocal-inverse

b^(-6)/(4*a*b)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(b^6*4*a*b)

⇒ algebra.manipulation.exponents.add-exponents

1/(4*b^7*a)

8.

(5*a)^(-2)*10*b^(-1)

⇒ algebra.manipulation.exponents.reciprocal-inverse

10*b^(-1)/(5*a)^2

⇒ algebra.manipulation.exponents.reciprocal-inverse

10/(b*(5*a)^2)

⇒ algebra.manipulation.exponents.distr-power

10/(b*25*a^2)

9.

4^(1/3)

⇒ algebra.manipulation.exponents.write-as-root

root 4 3

10.

5^(-1/4)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/5^(1/4)

⇒ algebra.manipulation.exponents.write-as-root

1/root 5 4

11.

5*a^(1/2)

⇒ algebra.manipulation.exponents.write-as-root

5*sqrt a

12.

3*a^(-1/4)

⇒ algebra.manipulation.exponents.reciprocal-inverse

3/a^(1/4)

⇒ algebra.manipulation.exponents.write-as-root

3/root a 4

13.

4/(a^(-1)*b^(1/3))

⇒ algebra.manipulation.exponents.reciprocal-inverse

4*a/b^(1/3)

⇒ algebra.manipulation.exponents.write-as-root

4*a/root b 3

14.

a^(-1)/(8*b^(-2/3))

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(a*8*b^(-2/3))

⇒ algebra.manipulation.exponents.reciprocal-inverse

b^(2/3)/(a*8)

⇒ algebra.manipulation.exponents.write-as-root

root (b^2) 3/(a*8)

15.

1/(3*a^(2/5)*b^(-1))

⇒ algebra.manipulation.exponents.reciprocal-inverse

b/(3*a^(2/5))

⇒ algebra.manipulation.exponents.write-as-root

b/(3*root (a^2) 5)

16.

3*a^(1/4)*b^(-1/2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

3*a^(1/4)/b^(1/2)

⇒ algebra.manipulation.exponents.write-as-root

3*root a 4/b^(1/2)

⇒ algebra.manipulation.exponents.write-as-root

3*root a 4/sqrt b

17.

a*b^(-2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

a/b^2

18.

a^(-1)*b^2

⇒ algebra.manipulation.exponents.reciprocal-inverse

b^2/a

19.

a^(-2)*b^(-3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

b^(-3)/a^2

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(b^3*a^2)

20.

1/a^(-3)*(b^(-2))^2

⇒ algebra.manipulation.exponents.mul-exponents

b^(-4)/a^(-3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(b^4*a^(-3))

⇒ algebra.manipulation.exponents.reciprocal-inverse

a^3/b^4

21.

1/(a*b)^(-2)*a*b^(-1)

⇒ algebra.manipulation.exponents.reciprocal-inverse

(a*b)^2*a*b^(-1)

⇒ algebra.manipulation.exponents.reciprocal-inverse

(a*b)^2*a/b

⇒ algebra.manipulation.exponents.distr-power

a^2*b^2*a/b

⇒ algebra.manipulation.exponents.add-exponents

a^3*b^2/b

⇒ algebra.manipulation.exponents.sub-exponents

a^3*b

22.

(2*a)^(-1)/(4*b)^(-2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(2*a*(4*b)^(-2))

⇒ algebra.manipulation.exponents.reciprocal-inverse

(4*b)^2/(2*a)

⇒ algebra.manipulation.exponents.distr-power

8*b^2/a

23.

(4*a*b)^(-1)*(b^2)^(-3)

⇒ algebra.manipulation.exponents.mul-exponents

(4*a*b)^(-1)*b^(-6)

⇒ algebra.manipulation.exponents.reciprocal-inverse

b^(-6)/(4*a*b)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(b^6*4*a*b)

⇒ algebra.manipulation.exponents.add-exponents

1/(4*b^7*a)

24.

(5*a)^(-2)*10*b^(-1)

⇒ algebra.manipulation.exponents.reciprocal-inverse

10*b^(-1)/(5*a)^2

⇒ algebra.manipulation.exponents.reciprocal-inverse

10/(b*(5*a)^2)

⇒ algebra.manipulation.exponents.distr-power

10/(b*25*a^2)

25.

2*a^(-2)*b^2

⇒ algebra.manipulation.exponents.reciprocal-inverse

2*b^2/a^2

26.

4*a^(-5)*b^3

⇒ algebra.manipulation.exponents.reciprocal-inverse

4*b^3/a^5

27.

3*a^2*b^(-1)

⇒ algebra.manipulation.exponents.reciprocal-inverse

3*a^2/b

28.

5*a*b^(-3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

5*a/b^3

29.

1/7*a^(-2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(a^2*7)

30.

1/3*a^(-4)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(a^4*3)

31.

1/5*a^(-6)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(a^6*5)

32.

1/2*a^(-3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(a^3*2)

33.

3*a^(-1)

⇒ algebra.manipulation.exponents.reciprocal-inverse

3/a

34.

4*a^(-4)

⇒ algebra.manipulation.exponents.reciprocal-inverse

4/a^4

35.

5*a^(-3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

5/a^3

36.

2*a^(-7)

⇒ algebra.manipulation.exponents.reciprocal-inverse

2/a^7

37.

(2/3*a)^(-3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(2/3*a)^3

⇒ algebra.manipulation.exponents.distr-power

27/(8*a^3)

38.

(3/4*a)^(-2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(3/4*a)^2

⇒ algebra.manipulation.exponents.distr-power

16/(9*a^2)

39.

(2/5*a)^(-3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(2/5*a)^3

⇒ algebra.manipulation.exponents.distr-power

125/(8*a^3)

40.

(5/6*a)^(-2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(5/6*a)^2

⇒ algebra.manipulation.exponents.distr-power

36/(25*a^2)

41.

(2*a)^(-3)*b^(-4)

⇒ algebra.manipulation.exponents.reciprocal-inverse

b^(-4)/(2*a)^3

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(b^4*(2*a)^3)

⇒ algebra.manipulation.exponents.distr-power

1/(b^4*8*a^3)

42.

4*a^(-2)*(3*b)^(-2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

4*(3*b)^(-2)/a^2

⇒ algebra.manipulation.exponents.reciprocal-inverse

4/((3*b)^2*a^2)

⇒ algebra.manipulation.exponents.distr-power

4/(9*b^2*a^2)

43.

(4*a)^(-3)*7*b^(-5)

⇒ algebra.manipulation.exponents.reciprocal-inverse

7*b^(-5)/(4*a)^3

⇒ algebra.manipulation.exponents.reciprocal-inverse

7/(b^5*(4*a)^3)

⇒ algebra.manipulation.exponents.distr-power

7/(b^5*64*a^3)

44.

9*a^(-7)*(2*b)^(-4)

⇒ algebra.manipulation.exponents.reciprocal-inverse

9*(2*b)^(-4)/a^7

⇒ algebra.manipulation.exponents.reciprocal-inverse

9/((2*b)^4*a^7)

⇒ algebra.manipulation.exponents.distr-power

9/(16*b^4*a^7)

45.

a^5/(2*b)^(-2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

a^5*(2*b)^2

⇒ algebra.manipulation.exponents.distr-power

4*a^5*b^2

46.

(2*a)^(-3)/b^2

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/((2*a)^3*b^2)

⇒ algebra.manipulation.exponents.distr-power

1/(8*a^3*b^2)

47.

a^(-3)/b^(-3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(a^3*b^(-3))

⇒ algebra.manipulation.exponents.reciprocal-inverse

b^3/a^3

48.

(4*a)^(-2)/b^(-4)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/((4*a)^2*b^(-4))

⇒ algebra.manipulation.exponents.reciprocal-inverse

b^4/(4*a)^2

⇒ algebra.manipulation.exponents.distr-power

b^4/(16*a^2)

49.

5*a^(1/2)

⇒ algebra.manipulation.exponents.write-as-root

5*sqrt a

50.

7*a^(1/3)

⇒ algebra.manipulation.exponents.write-as-root

7*root a 3

51.

(2*a)^(1/4)

⇒ algebra.manipulation.exponents.write-as-root

root (2*a) 4

⇒ algebra.manipulation.exponents.distr-power

root 2 4*root a 4

52.

(3*a)^(1/5)

⇒ algebra.manipulation.exponents.write-as-root

root (3*a) 5

⇒ algebra.manipulation.exponents.distr-power

root 3 5*root a 5

53.

4*a^(2/3)

⇒ algebra.manipulation.exponents.write-as-root

4*root (a^2) 3

54.

2*a^(3/4)

⇒ algebra.manipulation.exponents.write-as-root

2*root (a^3) 4

55.

3*a^(2/5)

⇒ algebra.manipulation.exponents.write-as-root

3*root (a^2) 5

56.

4*a^(3/5)

⇒ algebra.manipulation.exponents.write-as-root

4*root (a^3) 5

57.

6*a^(-1/2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

6/a^(1/2)

⇒ algebra.manipulation.exponents.write-as-root

6/sqrt a

58.

4*a^(-1/3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

4/a^(1/3)

⇒ algebra.manipulation.exponents.write-as-root

4/root a 3

59.

2*(3*a)^(-1/4)

⇒ algebra.manipulation.exponents.reciprocal-inverse

2/(3*a)^(1/4)

⇒ algebra.manipulation.exponents.write-as-root

2/root (3*a) 4

⇒ algebra.manipulation.exponents.distr-power

2/(root 3 4*root a 4)

60.

(3*a)^(-1/5)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(3*a)^(1/5)

⇒ algebra.manipulation.exponents.write-as-root

1/root (3*a) 5

⇒ algebra.manipulation.exponents.distr-power

1/(root 3 5*root a 5)

61.

5*a^(-2/3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

5/a^(2/3)

⇒ algebra.manipulation.exponents.write-as-root

5/root (a^2) 3

62.

7*a^(-3/4)

⇒ algebra.manipulation.exponents.reciprocal-inverse

7/a^(3/4)

⇒ algebra.manipulation.exponents.write-as-root

7/root (a^3) 4

63.

6*a^(-2/5)

⇒ algebra.manipulation.exponents.reciprocal-inverse

6/a^(2/5)

⇒ algebra.manipulation.exponents.write-as-root

6/root (a^2) 5

64.

2*a^(-3/7)

⇒ algebra.manipulation.exponents.reciprocal-inverse

2/a^(3/7)

⇒ algebra.manipulation.exponents.write-as-root

2/root (a^3) 7

65.

1/2*a^(1/3)*b^(-1/2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/2*a^(1/3)/b^(1/2)

⇒ algebra.manipulation.exponents.write-as-root

1/2*root a 3/b^(1/2)

⇒ algebra.manipulation.exponents.write-as-root

1/2*root a 3/sqrt b

66.

1/7*a^(-1/4)*b^(2/3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

b^(2/3)/(7*a^(1/4))

⇒ algebra.manipulation.exponents.write-as-root

root (b^2) 3/(7*a^(1/4))

⇒ algebra.manipulation.exponents.write-as-root

root (b^2) 3/(7*root a 4)

67.

4*a^(1/2)*b^(-1/5)

⇒ algebra.manipulation.exponents.reciprocal-inverse

4*a^(1/2)/b^(1/5)

⇒ algebra.manipulation.exponents.write-as-root

4*sqrt a/b^(1/5)

⇒ algebra.manipulation.exponents.write-as-root

4*sqrt a/root b 5

68.

3*a^(-3/5)*b^(1/3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

3*b^(1/3)/a^(3/5)

⇒ algebra.manipulation.exponents.write-as-root

3*root b 3/a^(3/5)

⇒ algebra.manipulation.exponents.write-as-root

3*root b 3/root (a^3) 5

69.

(2*a)^(-2/3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(2*a)^(2/3)

⇒ algebra.manipulation.exponents.write-as-root

1/root ((2*a)^2) 3

⇒ algebra.manipulation.exponents.distr-power

1/root (4*a^2) 3

⇒ algebra.manipulation.exponents.distr-power

1/(root 4 3*root (a^2) 3)

70.

(6*a)^(-2/5)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(6*a)^(2/5)

⇒ algebra.manipulation.exponents.write-as-root

1/root ((6*a)^2) 5

⇒ algebra.manipulation.exponents.distr-power

1/root (36*a^2) 5

⇒ algebra.manipulation.exponents.distr-power

1/(root 36 5*root (a^2) 5)

71.

(3*a)^(-3/5)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(3*a)^(3/5)

⇒ algebra.manipulation.exponents.write-as-root

1/root ((3*a)^3) 5

⇒ algebra.manipulation.exponents.distr-power

1/root (27*a^3) 5

⇒ algebra.manipulation.exponents.distr-power

1/(root 27 5*root (a^3) 5)

72.

(2*a)^(-4/7)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(2*a)^(4/7)

⇒ algebra.manipulation.exponents.write-as-root

1/root ((2*a)^4) 7

⇒ algebra.manipulation.exponents.distr-power

1/root (16*a^4) 7

⇒ algebra.manipulation.exponents.distr-power

1/(root 16 7*root (a^4) 7)

73.

2*a^(-2)*b^2

⇒ algebra.manipulation.exponents.reciprocal-inverse

2*b^2/a^2

74.

4*a^(-5)*b^3

⇒ algebra.manipulation.exponents.reciprocal-inverse

4*b^3/a^5

75.

3*a^2*b^(-1)

⇒ algebra.manipulation.exponents.reciprocal-inverse

3*a^2/b

76.

5*a*b^(-3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

5*a/b^3

77.

1/7*a^(-2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(a^2*7)

78.

1/3*a^(-4)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(a^4*3)

79.

1/5*a^(-6)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(a^6*5)

80.

1/2*a^(-3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(a^3*2)

81.

3*a^(-1)

⇒ algebra.manipulation.exponents.reciprocal-inverse

3/a

82.

4*a^(-4)

⇒ algebra.manipulation.exponents.reciprocal-inverse

4/a^4

83.

5*a^(-3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

5/a^3

84.

2*a^(-7)

⇒ algebra.manipulation.exponents.reciprocal-inverse

2/a^7

85.

(2/3*a)^(-3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(2/3*a)^3

⇒ algebra.manipulation.exponents.distr-power

27/(8*a^3)

86.

(3/4*a)^(-2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(3/4*a)^2

⇒ algebra.manipulation.exponents.distr-power

16/(9*a^2)

87.

(2/5*a)^(-3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(2/5*a)^3

⇒ algebra.manipulation.exponents.distr-power

125/(8*a^3)

88.

(5/6*a)^(-2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(5/6*a)^2

⇒ algebra.manipulation.exponents.distr-power

36/(25*a^2)

89.

(2*a)^(-3)*b^(-4)

⇒ algebra.manipulation.exponents.reciprocal-inverse

b^(-4)/(2*a)^3

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(b^4*(2*a)^3)

⇒ algebra.manipulation.exponents.distr-power

1/(b^4*8*a^3)

90.

4*a^(-2)*(3*b)^(-2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

4*(3*b)^(-2)/a^2

⇒ algebra.manipulation.exponents.reciprocal-inverse

4/((3*b)^2*a^2)

⇒ algebra.manipulation.exponents.distr-power

4/(9*b^2*a^2)

91.

(4*a)^(-3)*7*b^(-5)

⇒ algebra.manipulation.exponents.reciprocal-inverse

7*b^(-5)/(4*a)^3

⇒ algebra.manipulation.exponents.reciprocal-inverse

7/(b^5*(4*a)^3)

⇒ algebra.manipulation.exponents.distr-power

7/(b^5*64*a^3)

92.

9*a^(-7)*(2*b)^(-4)

⇒ algebra.manipulation.exponents.reciprocal-inverse

9*(2*b)^(-4)/a^7

⇒ algebra.manipulation.exponents.reciprocal-inverse

9/((2*b)^4*a^7)

⇒ algebra.manipulation.exponents.distr-power

9/(16*b^4*a^7)

93.

a^5/(2*b)^(-2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

a^5*(2*b)^2

⇒ algebra.manipulation.exponents.distr-power

4*a^5*b^2

94.

(2*a)^(-3)/b^2

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/((2*a)^3*b^2)

⇒ algebra.manipulation.exponents.distr-power

1/(8*a^3*b^2)

95.

a^(-3)/b^(-3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(a^3*b^(-3))

⇒ algebra.manipulation.exponents.reciprocal-inverse

b^3/a^3

96.

(4*a)^(-2)/b^(-4)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/((4*a)^2*b^(-4))

⇒ algebra.manipulation.exponents.reciprocal-inverse

b^4/(4*a)^2

⇒ algebra.manipulation.exponents.distr-power

b^4/(16*a^2)

97.

5*a^(1/2)

⇒ algebra.manipulation.exponents.write-as-root

5*sqrt a

98.

7*a^(1/3)

⇒ algebra.manipulation.exponents.write-as-root

7*root a 3

99.

(2*a)^(1/4)

⇒ algebra.manipulation.exponents.write-as-root

root (2*a) 4

⇒ algebra.manipulation.exponents.distr-power

root 2 4*root a 4

100.

(3*a)^(1/5)

⇒ algebra.manipulation.exponents.write-as-root

root (3*a) 5

⇒ algebra.manipulation.exponents.distr-power

root 3 5*root a 5

101.

(4*a)^(2/3)

⇒ algebra.manipulation.exponents.write-as-root

root ((4*a)^2) 3

⇒ algebra.manipulation.exponents.distr-power

root (16*a^2) 3

⇒ algebra.manipulation.exponents.distr-power

root 16 3*root (a^2) 3

102.

2*a^(3/4)

⇒ algebra.manipulation.exponents.write-as-root

2*root (a^3) 4

103.

(3*a)^(2/5)

⇒ algebra.manipulation.exponents.write-as-root

root ((3*a)^2) 5

⇒ algebra.manipulation.exponents.distr-power

root (9*a^2) 5

⇒ algebra.manipulation.exponents.distr-power

root 9 5*root (a^2) 5

104.

4*a^(3/5)

⇒ algebra.manipulation.exponents.write-as-root

4*root (a^3) 5

105.

6*a^(-1/2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

6/a^(1/2)

⇒ algebra.manipulation.exponents.write-as-root

6/sqrt a

106.

4*a^(-1/3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

4/a^(1/3)

⇒ algebra.manipulation.exponents.write-as-root

4/root a 3

107.

2*(3*a)^(-1/4)

⇒ algebra.manipulation.exponents.reciprocal-inverse

2/(3*a)^(1/4)

⇒ algebra.manipulation.exponents.write-as-root

2/root (3*a) 4

⇒ algebra.manipulation.exponents.distr-power

2/(root 3 4*root a 4)

108.

(3*a)^(-1/5)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(3*a)^(1/5)

⇒ algebra.manipulation.exponents.write-as-root

1/root (3*a) 5

⇒ algebra.manipulation.exponents.distr-power

1/(root 3 5*root a 5)

109.

5*a^(-2/3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

5/a^(2/3)

⇒ algebra.manipulation.exponents.write-as-root

5/root (a^2) 3

110.

7*a^(-3/4)

⇒ algebra.manipulation.exponents.reciprocal-inverse

7/a^(3/4)

⇒ algebra.manipulation.exponents.write-as-root

7/root (a^3) 4

111.

6*a^(-2/5)

⇒ algebra.manipulation.exponents.reciprocal-inverse

6/a^(2/5)

⇒ algebra.manipulation.exponents.write-as-root

6/root (a^2) 5

112.

2*a^(-3/7)

⇒ algebra.manipulation.exponents.reciprocal-inverse

2/a^(3/7)

⇒ algebra.manipulation.exponents.write-as-root

2/root (a^3) 7

113.

1/2*a^(1/3)*b^(-1/2)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/2*a^(1/3)/b^(1/2)

⇒ algebra.manipulation.exponents.write-as-root

1/2*root a 3/b^(1/2)

⇒ algebra.manipulation.exponents.write-as-root

1/2*root a 3/sqrt b

114.

1/7*a^(-1/4)*b^(2/3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

b^(2/3)/(7*a^(1/4))

⇒ algebra.manipulation.exponents.write-as-root

root (b^2) 3/(7*a^(1/4))

⇒ algebra.manipulation.exponents.write-as-root

root (b^2) 3/(7*root a 4)

115.

4*a^(1/2)*b^(-1/5)

⇒ algebra.manipulation.exponents.reciprocal-inverse

4*a^(1/2)/b^(1/5)

⇒ algebra.manipulation.exponents.write-as-root

4*sqrt a/b^(1/5)

⇒ algebra.manipulation.exponents.write-as-root

4*sqrt a/root b 5

116.

3*a^(-3/5)*b^(1/3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

3*b^(1/3)/a^(3/5)

⇒ algebra.manipulation.exponents.write-as-root

3*root b 3/a^(3/5)

⇒ algebra.manipulation.exponents.write-as-root

3*root b 3/root (a^3) 5

117.

(2*a)^(-2/3)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(2*a)^(2/3)

⇒ algebra.manipulation.exponents.write-as-root

1/root ((2*a)^2) 3

⇒ algebra.manipulation.exponents.distr-power

1/root (4*a^2) 3

⇒ algebra.manipulation.exponents.distr-power

1/(root 4 3*root (a^2) 3)

118.

(6*a)^(-2/5)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(6*a)^(2/5)

⇒ algebra.manipulation.exponents.write-as-root

1/root ((6*a)^2) 5

⇒ algebra.manipulation.exponents.distr-power

1/root (36*a^2) 5

⇒ algebra.manipulation.exponents.distr-power

1/(root 36 5*root (a^2) 5)

119.

(3*a)^(-3/5)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(3*a)^(3/5)

⇒ algebra.manipulation.exponents.write-as-root

1/root ((3*a)^3) 5

⇒ algebra.manipulation.exponents.distr-power

1/root (27*a^3) 5

⇒ algebra.manipulation.exponents.distr-power

1/(root 27 5*root (a^3) 5)

120.

(2*a)^(-4/7)

⇒ algebra.manipulation.exponents.reciprocal-inverse

1/(2*a)^(4/7)

⇒ algebra.manipulation.exponents.write-as-root

1/root ((2*a)^4) 7

⇒ algebra.manipulation.exponents.distr-power

1/root (16*a^4) 7

⇒ algebra.manipulation.exponents.distr-power

1/(root 16 7*root (a^4) 7)