Write with Rational (Fractional) Exponents ( eighth root of (4a)^3)^8

${(\sqrt[8]{{(4 a)}^{3}})}^{8}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[8]{{(4 a)}^{3}}$ as ${(4 a)}^{\frac{3}{8}}$ .

${({(4 a)}^{\frac{3}{8}})}^{8}$

Step 2

Multiply the exponents in ${({(4 a)}^{\frac{3}{8}})}^{8}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(4 a)}^{\frac{3}{8} \cdot 8}$

Cancel the common factor of $8$ .

Cancel the common factor.

${(4 a)}^{\frac{3}{8} \cdot 8}$

Rewrite the expression.

${(4 a)}^{3}$