Simplify ((w^(1/6))/(w^(-2/3)))^2

${(\frac{w^{\frac{1}{6}}}{w^{- \frac{2}{3}}})}^{2}$

Step 1

Move $w^{- \frac{2}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(w^{\frac{1}{6}} w^{\frac{2}{3}})}^{2}$

Step 2

Multiply $w^{\frac{1}{6}}$ by $w^{\frac{2}{3}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(w^{\frac{1}{6} + \frac{2}{3}})}^{2}$

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

${(w^{\frac{1}{6} + \frac{2}{3} \cdot \frac{2}{2}})}^{2}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

${(w^{\frac{1}{6} + \frac{2 \cdot 2}{3 \cdot 2}})}^{2}$

Multiply $3$ by $2$ .

${(w^{\frac{1}{6} + \frac{2 \cdot 2}{6}})}^{2}$

Combine the numerators over the common denominator.

${(w^{\frac{1 + 2 \cdot 2}{6}})}^{2}$

Simplify the numerator.

Multiply $2$ by $2$ .

${(w^{\frac{1 + 4}{6}})}^{2}$

Add $1$ and $4$ .

${(w^{\frac{5}{6}})}^{2}$

Step 3

Multiply the exponents in ${(w^{\frac{5}{6}})}^{2}$ .

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

$w^{\frac{5}{6} \cdot 2}$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$w^{\frac{5}{2 (3)} \cdot 2}$

Cancel the common factor.

$w^{\frac{5}{2 \cdot 3} \cdot 2}$

Rewrite the expression.

$w^{\frac{5}{3}}$