Question

type the correct answer in each box. use numerals instead of words. $7^\frac{1}{4}$
the expression above can also be written in the form $\sqrtb{a}$.
for this expression, $a = \square$ and $b = \square$ .

Explanation:

Step1: Recall rational exponent rule

For any positive real number $x$, $x^{\frac{m}{n}} = \sqrt[n]{x^m}$

Step2: Match given expression to rule

Given $7^{\frac{1}{4}}$, compare to $x^{\frac{m}{n}} = \sqrt[n]{x^m}$. Here $x=7$, $m=1$, $n=4$. So $7^{\frac{1}{4}} = \sqrt[4]{7^1} = \sqrt[4]{7}$

Step3: Identify $a$ and $b$

Compare $\sqrt[4]{7}$ to $\sqrt[b]{a}$. We get $a=7$, $b=4$

Answer:

$a=7$ and $b=4$