Answer the following questions about fractional exponents.

MATHEMATICS · Multi-part · AoPS · Mathematics · Follow the Rules · Follow the Rules

Problem

Answer the following questions about fractional exponents. (i) Explain why, for any positive real number

a

, the expression

a^{\tfrac{m}{n}}

can be written as

\sqrt[n]{a^{m}}

. (ii) Using the explanation in part (i), write

\sqrt[4]{27}

in the form

3^{p}

, where

p

is a rational number. (iii) Calculate the numerical value of

\sqrt[4]{27}

correct to three decimal places."