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.
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