SOLUTION: If a and b are positive and 16a^3 * b^-4 = 2a what is a^-2 in terms of b? (A) -8b (B) 1/(8b^4) (C) 8/(b^4) (D) 4b (E) 4b^4

Algebra ->  Equations -> SOLUTION: If a and b are positive and 16a^3 * b^-4 = 2a what is a^-2 in terms of b? (A) -8b (B) 1/(8b^4) (C) 8/(b^4) (D) 4b (E) 4b^4      Log On


   

Question 1202587: If a and b are positive and 16a^3 * b^-4 = 2a what is a^-2 in terms of b?
(A) -8b
(B) 1/(8b^4)
(C) 8/(b^4)
(D) 4b
(E) 4b^4
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


%2816a%5E3%29%28b%5E%28-4%29%29=2a

On both sides, multiply by b^4 and divide by 2a to separate the a's and b's.

8a%5E2=b%5E4

We want the value of a^-2; so take the reciprocal of both sides of the equation.

%281%2F%288a%5E2%29%29=%281%2Fb%5E4%29

Multiply by 8 to get the desired expression on the left.

%281%2Fa%5E2%29=8%2Fb%5E4

ANSWER: (C) 8%2Fb%5E4