Question

I cant figure out this problem. could really use some help

Answer 1

There are essentially three rules in these sorts of power multiplication problems:

`x^(-a) = (1)/(x^a)`

`x^a x^b = x^(a+ b)`

`(x^a)^b = x^(a b)`

These rules just tell us a negative exponent means the reciprocal of the same thing with a positive exponent, that when we multiply factors with the same base we add their exponents, and when we raise something to a power to another power we get to multiply the exponents.

Let's do the algebra before we substitute (we could do it either way).

`(p^2 q^(-3) )^(-2) (p^(-3)q^5)^(-2)`

`= (p^(-4) q^(6) ) (p^(6)q^(-10))`

`= p^(2) q^(-4)`

Substituting p=-2, q=-1

`= 2^(2) (-1)^(-4)`

`= 4 (1/(-1)^4) = 4\ (1/1) = 4`

Answer: 4, last choice