Question

Solve using fractional law exponent rule

Answer 1

Answer:

We conclude that:

$\sqrt[5]{8^3}=8^{\frac{3}{5}}$

Step-by-step explanation:

Given

We are given the expression

$\sqrt[5]{8^3}$

To determine

Solve using fractional law exponent rule

Given the expression

$\sqrt[5]{8^3}$

Apply radical rule:  $\sqrt[n]{a}=a^{\frac{1}{n}}$

$\sqrt[5]{8^3}=\left(8^3\right)^{\frac{1}{5}}$

Apply exponent rule:  $\left(a^b\right)^c=a^{bc}$

       $=8^{3\cdot \frac{1}{5}}$

Multiply the exponent:  3 × 1/5 = 3/5

     $=8^{\frac{3}{5}}$

Therefore, we conclude that:

$\sqrt[5]{8^3}=8^{\frac{3}{5}}$