Question

evaluate the expression.
$(4^{0} \cdot 3^{2})^{-2} = \square$

Explanation:

Step1: Simplify the zero exponent

Any non-zero number to the power of 0 is 1, so $4^0 = 1$.

Step2: Simplify the squared term

Calculate $3^2$: $3^2 = 9$.

Step3: Multiply the terms inside parentheses

Multiply the results from Step1 and Step2: $1 \times 9 = 9$.

Step4: Apply the negative exponent

A number to a negative exponent is the reciprocal of the number to the positive exponent: $9^{-2} = \frac{1}{9^2}$.

Step5: Calculate the final value

Compute $9^2 = 81$, so $\frac{1}{9^2} = \frac{1}{81}$.

Answer:

$\frac{1}{81}$