Simplify ((x^3y^n)/(z^(m+1)))^k

${(\frac{x^{3} y^{n}}{z^{m + 1}})}^{k}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{x^{3} y^{n}}{z^{m + 1}}$ .

$\frac{{(x^{3} y^{n})}^{k}}{{(z^{m + 1})}^{k}}$

Apply the product rule to $x^{3} y^{n}$ .

$\frac{{(x^{3})}^{k} {(y^{n})}^{k}}{{(z^{m + 1})}^{k}}$

Step 2

Simplify the numerator.

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

$\frac{x^{3 k} {(y^{n})}^{k}}{{(z^{m + 1})}^{k}}$

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

$\frac{x^{3 k} y^{n k}}{{(z^{m + 1})}^{k}}$

Step 3

Multiply the exponents in ${(z^{m + 1})}^{k}$ .

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

$\frac{x^{3 k} y^{n k}}{z^{(m + 1) k}}$

Apply the distributive property.

$\frac{x^{3 k} y^{n k}}{z^{m k + 1 k}}$

Multiply $k$ by $1$ .

$\frac{x^{3 k} y^{n k}}{z^{m k + k}}$