Which is the value of StartFraction 2 Superscript negative 3 Baseline over 3 Superscript negative 2 Baseline EndFraction?

Answer options with 5 options
A.
negative StartFraction 8 over 9 EndFraction

B.
negative StartFraction 2 over 3 EndFraction

C.
StartFraction 8 over 9 EndFraction

D.
StartFraction 9 over 8 EndFraction

E.
StartFraction 3 over 2 EndFraction

1 answer

To solve the expression \(\frac{2^{-3}}{3^{-2}}\), we can first rewrite it:

\[ \frac{2^{-3}}{3^{-2}} = 2^{-3} \cdot 3^{2} \]

Next, we simplify each part:

\[ 2^{-3} = \frac{1}{2^3} = \frac{1}{8} \] \[ 3^{2} = 9 \]

Now, we combine these results:

\[ 2^{-3} \cdot 3^{2} = \frac{1}{8} \cdot 9 = \frac{9}{8} \]

Thus, the value of \(\frac{2^{-3}}{3^{-2}}\) is \(\frac{9}{8}\).

The correct answer from the provided options is:

D. \(\frac{9}{8}\).