Question

what is another expression that I can use for this problem ?$\sqrt[c]{a ^{b} }$

Answer 1

The expression:

$7^{\frac{9}{4}}\text{ can be re}written\text{ once the laws of indices have b}een\text{ applied}$

Applying the fractional laws of indices, where the denominator becomes a root and the numerator an index.

$7^{\frac{9}{4}}=\sqrt[4]{7^9}$

Comparing the expression with,

$\begin{gathered} \sqrt[c]{a^b}\text{ } \\ \therefore\text{ }\sqrt[4]{7^9}\text{ =}\sqrt[c]{a^b} \end{gathered}$

Hence, a = 7, b = 9, c = 4