Simplify (125a^8)^(1/3)

${(125 a^{8})}^{\frac{1}{3}}$

Step 1

Simplify the expression.

Apply the product rule to $125 a^{8}$ .

$125^{\frac{1}{3}} {(a^{8})}^{\frac{1}{3}}$

Rewrite $125$ as $5^{3}$ .

${(5^{3})}^{\frac{1}{3}} {(a^{8})}^{\frac{1}{3}}$

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

$5^{3 (\frac{1}{3})} {(a^{8})}^{\frac{1}{3}}$

Step 2

Cancel the common factor of $3$ .

Cancel the common factor.

$5^{3 (\frac{1}{3})} {(a^{8})}^{\frac{1}{3}}$

Rewrite the expression.

$5^{1} {(a^{8})}^{\frac{1}{3}}$

Step 3

Evaluate the exponent.

$5 {(a^{8})}^{\frac{1}{3}}$

Step 4

Multiply the exponents in ${(a^{8})}^{\frac{1}{3}}$ .

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

$5 a^{8 (\frac{1}{3})}$

Combine $8$ and $\frac{1}{3}$ .

$5 a^{\frac{8}{3}}$