Simplify (a^6b^12)^(1/3)

${(a^{6} b^{12})}^{\frac{1}{3}}$

Step 1

Apply the product rule to $a^{6} b^{12}$ .

${(a^{6})}^{\frac{1}{3}} {(b^{12})}^{\frac{1}{3}}$

Step 2

Multiply the exponents in ${(a^{6})}^{\frac{1}{3}}$ .

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

$a^{6 (\frac{1}{3})} {(b^{12})}^{\frac{1}{3}}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$a^{3 (2) \frac{1}{3}} {(b^{12})}^{\frac{1}{3}}$

Cancel the common factor.

$a^{3 \cdot 2 \frac{1}{3}} {(b^{12})}^{\frac{1}{3}}$

Rewrite the expression.

$a^{2} {(b^{12})}^{\frac{1}{3}}$

Step 3

Multiply the exponents in ${(b^{12})}^{\frac{1}{3}}$ .

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

$a^{2} b^{12 (\frac{1}{3})}$

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

$a^{2} b^{3 (4) \frac{1}{3}}$

Cancel the common factor.

$a^{2} b^{3 \cdot 4 \frac{1}{3}}$

Rewrite the expression.

$a^{2} b^{4}$