Answer:
We conclude that:
[tex]\sqrt[5]{8^3}=8^{\frac{3}{5}}[/tex]
Step-by-step explanation:
Given
We are given the expression
[tex]\sqrt[5]{8^3}[/tex]
To determine
Solve using fractional law exponent rule
Given the expression
[tex]\sqrt[5]{8^3}[/tex]
Apply radical rule: [tex]\sqrt[n]{a}=a^{\frac{1}{n}}[/tex]
[tex]\sqrt[5]{8^3}=\left(8^3\right)^{\frac{1}{5}}[/tex]
Apply exponent rule: [tex]\left(a^b\right)^c=a^{bc}[/tex]
[tex]=8^{3\cdot \frac{1}{5}}[/tex]
Multiply the exponent: 3 × 1/5 = 3/5
[tex]=8^{\frac{3}{5}}[/tex]
Therefore, we conclude that:
[tex]\sqrt[5]{8^3}=8^{\frac{3}{5}}[/tex]
