# How do you evaluate (5x ^ { - 3} y ) ( 6x ^ { 7} y ^ { - 4} )?

Oct 30, 2017

(5x^(-3)y)(6x^7y^(-4))=color(blue)((30x^4)/(y^3)

#### Explanation:

Simplify:

$\left(5 {x}^{- 3} y\right) \left(6 {x}^{7} {y}^{- 4}\right)$

Simplify the parentheses.

$5 {x}^{- 3} y \times 6 {x}^{7} {y}^{- 4}$

Multiply $5$ and $6$.

$30 {x}^{- 3} y {x}^{7} {y}^{- 4}$

Gather like variables.

$30 {x}^{- 3} {x}^{7} y {y}^{- 4}$

Apply the product rule of exponents: ${a}^{m} {a}^{n} = {a}^{m + n}$. (No exponent is understood to be $1$.

$30 {x}^{- 3 + 7} {y}^{1 - 4}$

Simplify.

$30 {x}^{4} {y}^{- 3}$

Apply the negative exponent rule: ${a}^{- m} = \frac{1}{a} ^ m$.

$\frac{30 {x}^{4}}{{y}^{3}}$ $\leftarrow$ Answer