Simplify (3x^2yz^3)^3

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

Step 1

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

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

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

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

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

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

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

Step 2

Raise $3$ to the power of $3$ .

$27 {(x^{2})}^{3} y^{3} {(z^{3})}^{3}$

Step 3

Multiply the exponents in ${(x^{2})}^{3}$ .

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

$27 x^{2 \cdot 3} y^{3} {(z^{3})}^{3}$

Multiply $2$ by $3$ .

$27 x^{6} y^{3} {(z^{3})}^{3}$

Step 4

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

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

$27 x^{6} y^{3} z^{3 \cdot 3}$

Multiply $3$ by $3$ .

$27 x^{6} y^{3} z^{9}$