Question

When I write my expression in rational exponent form, what is the fraction that goes with the base of 10?

Answer 1

Answer: Choice A

$\sqrt[4]{3^3}$

The fourth root of 3^3

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Explanation:

The exponent of 1/4 means "fourth root", so,

$3^{1/4} = \sqrt[4]{3}$

The outer exponent 3 can be moved inward like this

$\left(3^{1/4}\right)^3 = 3^{1/4*3} = 3^{3/4}$

Then we can use the rule

$x^{m/n} = \sqrt[n]{x^m}$

This means

$3^{3/4} = \sqrt[4]{3^3}$