Question

Raise the quality in parentheses to the indicated exponent, and slim lift 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:

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

SImplifying:

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

Answer:

$- \frac {1} {4x ^ {10} y ^ {4}}$