Simplify the Radical Expression ((w^7)/(w^4))^(5/12)

${(\frac{w^{7}}{w^{4}})}^{\frac{5}{12}}$

Cancel the common factor of $w^{7}$ and $w^{4}$ .

Factor $w^{4}$ out of $w^{7}$ .

${(\frac{w^{4} w^{3}}{w^{4}})}^{\frac{5}{12}}$

Cancel the common factors.

Multiply by $1$ .

${(\frac{w^{4} w^{3}}{w^{4} \cdot 1})}^{\frac{5}{12}}$

Cancel the common factor.

${(\frac{w^{4} w^{3}}{w^{4} \cdot 1})}^{\frac{5}{12}}$

Rewrite the expression.

${(\frac{w^{3}}{1})}^{\frac{5}{12}}$

Divide $w^{3}$ by $1$ .

${(w^{3})}^{\frac{5}{12}}$

Multiply the exponents in ${(w^{3})}^{\frac{5}{12}}$ .

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

$w^{3 (\frac{5}{12})}$

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

$w^{3 \frac{5}{3 (4)}}$

Cancel the common factor.

$w^{3 \frac{5}{3 \cdot 4}}$

Rewrite the expression.

$w^{\frac{5}{4}}$