Simplify (y^4)^(1/6)

${(y^{4})}^{\frac{1}{6}}$

Step 1

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

$y^{4 (\frac{1}{6})}$

Step 2

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$y^{2 (2) \frac{1}{6}}$

Factor $2$ out of $6$ .

$y^{2 \cdot 2 \frac{1}{2 \cdot 3}}$

Cancel the common factor.

$y^{2 \cdot 2 \frac{1}{2 \cdot 3}}$

Rewrite the expression.

$y^{2 (\frac{1}{3})}$

Step 3

Combine $2$ and $\frac{1}{3}$ .

$y^{\frac{2}{3}}$