Question

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

Answer 1

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))`