Simplify ((w^5)/w)^(1/14)

${(\frac{w^{5}}{w})}^{\frac{1}{14}}$

Step 1

Cancel the common factor of $w^{5}$ and $w$ .

Factor $w$ out of $w^{5}$ .

${(\frac{w \cdot w^{4}}{w})}^{\frac{1}{14}}$

Cancel the common factors.

Raise $w$ to the power of $1$ .

${(\frac{w \cdot w^{4}}{w^{1}})}^{\frac{1}{14}}$

Factor $w$ out of $w^{1}$ .

${(\frac{w \cdot w^{4}}{w \cdot 1})}^{\frac{1}{14}}$

Cancel the common factor.

${(\frac{w \cdot w^{4}}{w \cdot 1})}^{\frac{1}{14}}$

Rewrite the expression.

${(\frac{w^{4}}{1})}^{\frac{1}{14}}$

Divide $w^{4}$ by $1$ .

${(w^{4})}^{\frac{1}{14}}$

Step 2

Multiply the exponents in ${(w^{4})}^{\frac{1}{14}}$ .

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

$w^{4 (\frac{1}{14})}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$w^{2 (2) \frac{1}{14}}$

Factor $2$ out of $14$ .

$w^{2 \cdot 2 \frac{1}{2 \cdot 7}}$

Cancel the common factor.

$w^{2 \cdot 2 \frac{1}{2 \cdot 7}}$

Rewrite the expression.

$w^{2 (\frac{1}{7})}$

Combine $2$ and $\frac{1}{7}$ .

$w^{\frac{2}{7}}$