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

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Answer 1 · 2018-03-27T06:12:10

$( x^41 )/(3^21 y^52$

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
To multiply exponents, you add

$(3^9 x^56 y^6 )/(3^30 x^15 y^58$

5) Reduce by cancelling
To divide exponents, you subtract

$( x^(56-15) )/(3^(30-9) y^(58-6)$

same as

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

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