Simplify (x^9yz^4)^5

${(x^{9} y z^{4})}^{5}$

Step 1

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

Apply the product rule to $x^{9} y z^{4}$ .

${(x^{9} y)}^{5} {(z^{4})}^{5}$

Apply the product rule to $x^{9} y$ .

${(x^{9})}^{5} y^{5} {(z^{4})}^{5}$

Step 2

Multiply the exponents in ${(x^{9})}^{5}$ .

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

$x^{9 \cdot 5} y^{5} {(z^{4})}^{5}$

Multiply $9$ by $5$ .

$x^{45} y^{5} {(z^{4})}^{5}$

Step 3

Multiply the exponents in ${(z^{4})}^{5}$ .

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

$x^{45} y^{5} z^{4 \cdot 5}$

Multiply $4$ by $5$ .

$x^{45} y^{5} z^{20}$