Simplify (3x^5z)^5

${(3 x^{5} z)}^{5}$

Step 1

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

Apply the product rule to $3 x^{5} z$ .

${(3 x^{5})}^{5} z^{5}$

Apply the product rule to $3 x^{5}$ .

$3^{5} {(x^{5})}^{5} z^{5}$

Step 2

Raise $3$ to the power of $5$ .

$243 {(x^{5})}^{5} z^{5}$

Step 3

Multiply the exponents in ${(x^{5})}^{5}$ .

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

$243 x^{5 \cdot 5} z^{5}$

Multiply $5$ by $5$ .

$243 x^{25} z^{5}$