Answer
$\sqrt[21]{7^{10}}$
Work Step by Step
Recall the rational exponent property (pg. 382):
$\sqrt[n]{a}=a^{\frac{1}{n}}$
Applying this property, we get:
$=7^{\frac{1}{7}}7^{\frac{1}{3}}$
Next, recall the basic exponent property (pg. 360):
$a^ma^n=a^{m+n}$
Applying this property to our last equation, we get:
$=7^{\frac{1}{7}+\frac{1}{3}}$
$=7^{\frac{3}{21}+\frac{7}{21}}$
$=7^{\frac{3+7}{21}}$
$=7^{\frac{10}{21}}$
Now, recall the rational exponent property (pg. 382):
$a^{\frac{m}{n}}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$
We use this property to rewrite the result as a radical:
$7^{\frac{10}{21}}=\sqrt[21]{7^{10}}$
