Simplify (x^5y^2z^8)/((xy)^-3)

$\frac{x^{5} y^{2} z^{8}}{{(x y)}^{- 3}}$

Step 1

Move ${(x y)}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$x^{5} y^{2} z^{8} {(x y)}^{3}$

Step 2

Apply the product rule to $x y$ .

$x^{5} y^{2} z^{8} (x^{3} y^{3})$

Step 3

Multiply $x^{5}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$x^{3} x^{5} y^{2} z^{8} y^{3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{3 + 5} y^{2} z^{8} y^{3}$

Add $3$ and $5$ .

$x^{8} y^{2} z^{8} y^{3}$

Step 4

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$x^{8} (y^{3} y^{2}) z^{8}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{8} y^{3 + 2} z^{8}$

Add $3$ and $2$ .

$x^{8} y^{5} z^{8}$