Question

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

103−−−√5

Answer 1

Answer: Choice A

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

The fourth root of 3^3

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Step-by-step 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}`