# How do you simplify (x^-4)^5(x^3y^2)^5?

Nov 1, 2015

${x}^{- 5} {y}^{10}$

#### Explanation:

First rule to use: the power of powers means to multiply the exponents, so

1. ${\left({x}^{- 4}\right)}^{5} = {x}^{- 4 \cdot 5} = {x}^{- 20}$
2. ${\left({x}^{3} {y}^{2}\right)}^{5} = {x}^{3 \cdot 5} {y}^{2 \cdot 5} = {x}^{15} {y}^{10}$

${x}^{- 20} \cdot {x}^{15} {y}^{10}$
Second rule to use: the product of powers with the same base means to sum the exponents. So, the $y$ power is alone and we'll leave it untouched. As for the $x$ powers, we have
${x}^{- 20} \cdot {x}^{15} = {x}^{- 20 + 15} = {x}^{- 5}$.