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Raise the quality in parentheses to the indicated exponent, and simplify the resulting expression with positive exponents.

Raise the quality in parentheses to the indicated exponent, and simplify the resulting-example-1
User Skatch
by
8.4k points

1 Answer

5 votes

For this case we have the following expression:


(\frac {-27x ^ 0 * y ^ {- 2}} {54x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =

By definition we have to:


a^0 = 1

So:


(\frac {-27y ^ {- 2}} {54x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =

Simplifying:


(\frac {-y ^ {- 2}} {2x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =

By definition of power properties we have to:


(a ^ n) ^ m = a ^ {n * m}

So, rewriting the expression we have:


(-1)^(-2)(-y^(-2*-2))/(2^(-2)*x^(-5*-2)*y^(-4*-2))=\\(1)/((-1)^2)*(-y^(4))/(2^(-2)x^(10)*y^(8))=

SImplifying:


+1*(y^(4-8))/(2^(-2)x^(10))=\\(y^(-4))/(2^(-2)x^(10))=\\(2^2)/(x^(10)y^(4))

Answer:


(4)/(x^(10)y^(4))

User Billy Liu
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