SOLUTION: Raise the quantity in parentheses to the indicated exponent, and simplify the resulting expression. Express answers with positive exponents. (-27x^0y^-2/54x^-5y^-4)^-2

Question 615569: Raise the quantity in parentheses to the indicated exponent, and simplify the resulting expression. Express answers with positive exponents.

(-27x^0y^-2/54x^-5y^-4)^-2

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

According to the order of operations (aka PEMDAS), we are allowed to perform operations inside a set of parentheses first. Since simplifying inside the parentheses makes this problem much easier, that is where I'll start. (If you really have to raise the quantity in the parentheses first, as the wording suggests, then re-post your question.)

First I will reduce the fraction. Since 2*27 = 54 the coefficients will reduce. And we can use the rule for exponents when dividing (i.e. subtract the exponents) on the variables:

This is a much easier expression to raise to the -2 power.

We can raise the expression to the -2 power by using the rules:

on the fraction as a whole; and
on the numerator.

Since -1 to any even power, including negative even powers, is 1 this becomes:

Using the rule for exponents that tells us to multiply the exponents when raising a power to a power, we can raise the x's and y's to the -2 power:

Since and we can see that a negative exponent means, in essence, a reciprocal. So we can rewrite expressions with negative exponents as a reciprocal with a positive exponent. And if our expressions with the negative exponents are in a fraction, they will "move" to the other "half". (Numerators will move to the denominator and denominators will move the to numerator.) Since everything in our expression has a negative exponent, everything is going to "move to the other half" when we rewrite with positive exponents:

And since 2 squared is 4:

This is the simplified expression. (This is the correct answer no matter how you simplify the expression and rewrite with positive exponents.)
RELATED QUESTIONS
Short Answer: Raise the quantity in parentheses to the indicated exponent, and simplify... (answered by stanbon)

Short Answer: Raise the quantity in parentheses to the indicated exponent, and simplify... (answered by Alan3354,stanbon)

Short Answer: Raise the quantity in parentheses to the indicated exponent, and simplify... (answered by Alan3354)

Raise the quantity in parentheses to the indicated exponent, and simplify the resulting... (answered by mananth)

Raise the quantity in parentheses to the indicated exponent, and simplify the resulting... (answered by stanbon)

Raise the quantity in the parentheses to the indicated exponent and simplify the... (answered by saifoo.khan)

Raise the quantity in parentheses to the indicated exponent, and simplify the resulting... (answered by stanbon)

short answer raise the quanity in parentheses to the indicated exponent, and simplify the (answered by Alan3354)

raise the quanity in parentheses to the indicated exponent and simplify the resulting... (answered by ankor@dixie-net.com)