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

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

Step 1

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

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

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

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

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

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

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

Step 2

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

$16 {(x^{2})}^{4} {(y^{3})}^{4} z^{4}$

Step 3

Multiply the exponents in ${(x^{2})}^{4}$ .

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

$16 x^{2 \cdot 4} {(y^{3})}^{4} z^{4}$

Multiply $2$ by $4$ .

$16 x^{8} {(y^{3})}^{4} z^{4}$

Step 4

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

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

$16 x^{8} y^{3 \cdot 4} z^{4}$

Multiply $3$ by $4$ .

$16 x^{8} y^{12} z^{4}$