Question

(3/8)^-2 = 64/9 show all work

Answer 1

To solve \( \left( \frac{3}{8} \right)^{-2} = \frac{64}{9} \), we'll start by applying the negative exponent rule, which states that \( a^{-n} = \frac{1}{a^n} \).

### Step 1: Apply the Negative Exponent Rule
\[
\left( \frac{3}{8} \right)^{-2} = \frac{1}{\left( \frac{3}{8} \right)^{2}}
\]

### Step 2: Compute \( \left( \frac{3}{8} \right)^{2} \)
\[
\left( \frac{3}{8} \right)^{2} = \frac{3^{2}}{8^{2}} = \frac{9}{64}
\]

### Step 3: Substitute Back into the Original Expression
\[
\left( \frac{3}{8} \right)^{-2} = \frac{1}{\frac{9}{64}} = \frac{64}{9}
\]

### Conclusion
Thus,

\[
\left( \frac{3}{8} \right)^{-2} = \frac{64}{9}
\]

Therefore, the original equation \( \left( \frac{3}{8} \right)^{-2} = \frac{64}{9} \) is verified to be true.