# How do you simplify ((3^-2 x^5 y^-5)^10 (3^3 x^-5 y^2)^3)/((3^5 x^-3 y^4)^2)?

Mar 27, 2018

( x^41 )/(3^21 y^52

#### Explanation:

Simplify

((3^-2 x^5 y^-5)^10  (3^3 x^-5 y^2)^3)/((3^5 x^-3  y^4)^2)

This problem isn't hard conceptually; it's just painstaking.

1) Clear the parentheses by raising all the powers inside the parentheses by the powers outside.
To raise a power to a power, you multiply.

(3^-20  x^50  y^-50  3^9  x^-15  y^6)/(3^10  x^-6  y^8

2) Clear the negative exponents by flipping them to the opposite side of the fraction bar and reversing the negative signs to positive

( x^50   3^9   y^6   x^6)/(3^10   y^8  3^20   y^50   x^15

3) Group like bases to make it easier to multiply them

(3^9    x^50 x^6    y^6 )/(3^10 3^20    x^15    y^8 y^50

4) Multiply like bases

(3^9  x^56  y^6 )/(3^30  x^15  y^58

5) Reduce by cancelling
To divide exponents, you subtract

( x^(56-15) )/(3^(30-9)  y^(58-6)

same as

( x^41 )/(3^21  y^52 $\leftarrow$ answer