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

To evaluate the expression

\[
\left( \frac{3a^{-3}b^2}{2a^{-1}b^0} \right)^2
\]

when \( a = -2 \) and \( b = -3 \), we first need to substitute the values of \( a \) and \( b \) into the expression.

1. Substitute \( a = -2 \) and \( b = -3 \):
- \( a^{-3} = (-2)^{-3} = -\frac{1}{8} \)
- \( b^2 = (-3)^2 = 9 \)
- \( a^{-1} = (-2)^{-1} = -\frac{1}{2} \)
- \( b^0 = (-3)^0 = 1 \)

2. Compute the numerator:
\[
3a^{-3}b^2 = 3 \left( -\frac{1}{8} \right)(9) = 3 \times -\frac{9}{8} = -\frac{27}{8}
\]

3. Compute the denominator:
\[
2a^{-1}b^0 = 2 \left( -\frac{1}{2} \right)(1) = -1
\]

4. Now form the complete fraction:
\[
\frac{-\frac{27}{8}}{-1} = \frac{27}{8}
\]

5. Finally, we need to square this fraction:
\[
\left( \frac{27}{8} \right)^2 = \frac{27^2}{8^2} = \frac{729}{64}
\]

Thus, the value of the entire expression is

\[
\frac{729}{64}
\]

So, the answer is

\[
\boxed{\frac{729}{64}}
\]