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

Question

asked Apr 18, 2020 115k views

1 Answer

Billy Liu · Answer 1 · 2020-04-23T07:29:54+0000

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: