Question

Which is the value of this expression when a = negative 2 and b = negative 3?

(StartFraction 3 a Superscript negative 3 Baseline b squared Over 2 a Superscript negative 1 Baseline b Superscript 0 Baseline EndFraction) squared
StartFraction 4 Over 9 EndFraction
StartFraction 27 Over 8 EndFraction
StartFraction 243 Over 32 EndFraction
StartFraction 729 Over 64 EndFraction

Answer 1

Compute inside the parentheses first:

(3 a^{-3} b^2) / (2 a^{-1} b^0) = (3/2) a^{-3 - (-1)} b^{2-0} = (3/2) a^{-2} b^2.

Square it:
[(3/2) a^{-2} b^2]^2 = (9/4) a^{-4} b^4.

Now substitute a = -2, b = -3:
a^{-4} = 1/(-2)^4 = 1/16, b^4 = (-3)^4 = 81.

So value = (9/4) * (1/16) * 81 = 729/64.

Answer: 729/64.