Question

6. Rewrite each of the following expressions without roots by using fractional exponents.

Please help! I have tried to look it up everywhere and I don’t understand how to do it. Anything helps!!

Answer 1

A. x¹/²

B. x¹/³

C. x¹/⁷

D. x⁵/²

E. x¹¹/³

F. 1 / x¹/⁴

G. 1 / x²/³

H. 1 / x⁹/²

Explanation:

A. √x

Recall

√M = M¹/²

Therefore,

√x = x¹/²

B. ³√x

Recall

ⁿ√M = M¹/ⁿ

Therefore,

³√x = x¹/³

C. ⁷√x

Recall

ⁿ√M = M¹/ⁿ

Therefore,

⁷√x = x¹/⁷

D. √x⁵

Recall

√Mⁿ = Mⁿ/²

Therefore,

√x⁵ = x⁵/²

E. ³√x¹¹

Recall

ⁿ√Mᵃ = Mᵃ/ⁿ

Therefore,

³√x¹¹ = x¹¹/³

F. 1 / ⁴√x

Recall

ⁿ√M = M¹/ⁿ

Therefore,

1 / ⁴√x = 1 / x¹/⁴

G. 1 / ³√x²

Recall

ⁿ√Mᵃ = Mᵃ/ⁿ

Therefore,

1 / ³√x² = 1 / x²/³

H. 1 / √x⁹

Recall

√Mⁿ = Mⁿ/²

Therefore,

1 / √x⁹ = 1 / x⁹/²