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:

$(-1)^{-2}\frac{-y^{-2*-2}}{2^{-2}*x^{-5*-2}*y^{-4*-2}}=\\\frac{1}{(-1)^2}*\frac{-y^{4}}{2^{-2}x^{10}*y^{8}}=$

SImplifying:

$+1*\frac{y^{4-8}}{2^{-2}x^{10}}=\\\frac{y^{-4}}{2^{-2}x^{10}}=\\\frac{2^2}{x^{10}y^{4}}$

Answer:

$\frac{4}{x^{10}y^{4}}$