Simplify ((2x^3y^4)/(z^3))^4

${(\frac{2 x^{3} y^{4}}{z^{3}})}^{4}$

Step 1

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

Apply the product rule to $\frac{2 x^{3} y^{4}}{z^{3}}$ .

$\frac{{(2 x^{3} y^{4})}^{4}}{{(z^{3})}^{4}}$

Apply the product rule to $2 x^{3} y^{4}$ .

$\frac{{(2 x^{3})}^{4} {(y^{4})}^{4}}{{(z^{3})}^{4}}$

Apply the product rule to $2 x^{3}$ .

$\frac{2^{4} {(x^{3})}^{4} {(y^{4})}^{4}}{{(z^{3})}^{4}}$

Step 2

Simplify the numerator.

Raise $2$ to the power of $4$ .

$\frac{16 {(x^{3})}^{4} {(y^{4})}^{4}}{{(z^{3})}^{4}}$

Multiply the exponents in ${(x^{3})}^{4}$ .

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

$\frac{16 x^{3 \cdot 4} {(y^{4})}^{4}}{{(z^{3})}^{4}}$

Multiply $3$ by $4$ .

$\frac{16 x^{12} {(y^{4})}^{4}}{{(z^{3})}^{4}}$

Multiply the exponents in ${(y^{4})}^{4}$ .

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

$\frac{16 x^{12} y^{4 \cdot 4}}{{(z^{3})}^{4}}$

Multiply $4$ by $4$ .

$\frac{16 x^{12} y^{16}}{{(z^{3})}^{4}}$

Step 3

Multiply the exponents in ${(z^{3})}^{4}$ .

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

$\frac{16 x^{12} y^{16}}{z^{3 \cdot 4}}$

Multiply $3$ by $4$ .

$\frac{16 x^{12} y^{16}}{z^{12}}$