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


103−−−√5

When I write my expression in rational exponent form what is the fraction that goes with the base of 101035 class=

Respuesta :

Answer: Choice A

[tex]\sqrt[4]{3^3}[/tex]

The fourth root of 3^3

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Explanation:

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

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

The outer exponent 3 can be moved inward like this

[tex]\left(3^{1/4}\right)^3 = 3^{1/4*3} = 3^{3/4}[/tex]

Then we can use the rule

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

This means

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