Mathematics: Solve using fractional law exponent rule

Is it 43(7) that is what i believe the number is...

Solve using fractional law exponent rule - id10450092, justinamber89

JayceMeyers06

17.03.2022

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:

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

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