Questions: Simplify (2^3)^-2.

Transcript text: Simplify $\left(2^{3}\right)^{-2}$.

Solution

Step 1: Evaluate the Exponent Inside the Parentheses

First, evaluate the expression inside the parentheses: $2^3$.

\[ 2^3 = 2 \times 2 \times 2 = 8 \]

Step 2: Apply the Negative Exponent

Next, apply the negative exponent to the result from Step 1. We have $(8)^{-2}$.

A negative exponent indicates the reciprocal of the base raised to the positive of that exponent:

\[ (8)^{-2} = \frac{1}{8^2} \]

Step 3: Evaluate the Exponent in the Denominator

Now, calculate $8^2$:

\[ 8^2 = 8 \times 8 = 64 \]

Substitute back into the expression:

\[ (8)^{-2} = \frac{1}{64} \]

Thus, the simplified form of $\left(2^{3}\right)^{-2}$ is $\boxed{\frac{1}{64}}$.

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