Answer:
We conclude that:
![\sqrt[5]{8^3}=8^{(3)/(5)}](https://img.qammunity.org/2022/formulas/mathematics/high-school/u1wam6pqhj0q69d4ldph5q5t0u8dqq8xxx.png)
Explanation:
Given
We are given the expression
![\sqrt[5]{8^3}](https://img.qammunity.org/2022/formulas/mathematics/high-school/fqeo42f1hn0kdncz94of5k8mjtp7yutdh5.png)
To determine
Solve using fractional law exponent rule
Given the expression
![\sqrt[5]{8^3}](https://img.qammunity.org/2022/formulas/mathematics/high-school/fqeo42f1hn0kdncz94of5k8mjtp7yutdh5.png)
Apply radical rule:
![\sqrt[n]{a}=a^{(1)/(n)}](https://img.qammunity.org/2022/formulas/mathematics/high-school/8zxcnirg8d32krxfdfe77dmcpm34xa9g9v.png)
![\sqrt[5]{8^3}=\left(8^3\right)^{(1)/(5)}](https://img.qammunity.org/2022/formulas/mathematics/high-school/c0s41yjqszks0g3h3llinduw6yyzittth8.png)
Apply exponent rule:


Multiply the exponent: 3 Ă— 1/5 = 3/5

Therefore, we conclude that:
![\sqrt[5]{8^3}=8^{(3)/(5)}](https://img.qammunity.org/2022/formulas/mathematics/high-school/u1wam6pqhj0q69d4ldph5q5t0u8dqq8xxx.png)