# How do you simplify ((x^-3y^-8)/(x^4y^-2))^-7 and write it using only positive exponents?

Jun 2, 2017

${\left(\frac{{x}^{- 3} {y}^{- 8}}{{x}^{4} {y}^{- 2}}\right)}^{- 7}$ simplified is color(blue)(x^(49)y^(42)

See the process in the explanation.

#### Explanation:

Simplify:

${\left(\frac{{x}^{- 3} {y}^{- 8}}{{x}^{4} {y}^{- 2}}\right)}^{- 7}$

Apply the power rule of exponents: ${\left({a}^{m}\right)}^{n} = {a}^{m \cdot n}$.

$\frac{{x}^{- 3 \cdot - 7} {y}^{- 8 \cdot - 7}}{{x}^{4 \cdot - 7} {y}^{- 2 \cdot - 7}}$

Simplify.

$\frac{{x}^{21} {y}^{56}}{{x}^{- 28} {y}^{14}}$

Apply the quotient rule of exponents: $\frac{{a}^{m}}{{a}^{n}} = {a}^{m - n}$.

${x}^{\left(21\right) - \left(- 28\right)} {y}^{56 - 14}$

Simplify.

${x}^{49} {y}^{42}$