# Simplify using the laws of exponents, then evaluate ((4^4m^3)/(3^3x^2))^4 x ((3^2x^3)/(4^3m))^5Everytime i try solving this equation, i get the wrong answer. please evaluate so i can compare...

Simplify using the laws of exponents, then evaluate

((4^4m^3)/(3^3x^2))^4 x ((3^2x^3)/(4^3m))^5

Everytime i try solving this equation, i get the wrong answer. please evaluate so i can compare it to my answer and see where i keep messing up

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Expert Answers

samhouston | Certified Educator

According to the laws of exponents:

- (n^a) * (n^b) = n^(a + b)
- (n^a) / (n^b) = n^(a - b)
- (n^a)^b = n^(a*b)

Numerator of first fraction: (4^4 * m^3)^4 = 4^16 * m^12

Denominator of first fraction: (3^3 * x^2)^4 = 3^12 * x^8

Numerator of second fraction: (3^2 * x^3)^5 = 3^10 * x^15

Denominator of second fraction: (4^3 * m)^5 = 4^15 * m^5

You can cross simplify.

4^16 / 4^15 = 4

3^10 / 3^12 = 3^-2 = 1/9

m^12 / m^5 = m^7

x^15 / x^8 = x^7

Put it all together.

4/9 * m^7 * x^7