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

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

Step 1

Apply the product rule to $a^{\frac{1}{6}} b^{\frac{1}{3}}$ .

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

Step 2

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

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

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

Cancel the common factor of $6$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Simplify.

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

Step 4

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

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

$a b^{\frac{1}{3} \cdot 6}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$a b^{2}$