# How do you simplify (8x^3y^-5)/(2(4x)^-1y^2) and write it using only positive exponents?

Nov 7, 2016

$\frac{16 {x}^{4}}{y} ^ 7$

#### Explanation:

Using the $\textcolor{b l u e}{\text{laws of exponents}}$

color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(a^-mhArr1/a^m" and " a^mxxa^n=a^(m+n))color(white)(2/2)|)))

We can write the expression as.

$\frac{8}{2} \times \left({x}^{3} \times {\left(4 x\right)}^{1}\right) \times {y}^{-} \frac{5}{y} ^ 2$

$= 4 \times 4 {x}^{4} \times \frac{1}{{y}^{2} \times {y}^{5}}$

$= \frac{16 {x}^{4}}{y} ^ 7$