Question

1. which expression is equivalent to $(8^2)^{-4}$? (4 poi)

options: $\frac{1}{8^2}$, $\frac{-1}{8cdot8cdot8cdot8cdot8cdot8cdot8cdot8}$, $8^2$, $\frac{1}{8cdot8cdot8cdot8cdot8cdot8cdot8cdot8}$

Explanation:

Step1: Apply power of a power rule

$(8^2)^{-4} = 8^{2 \times (-4)} = 8^{-8}$

Step2: Apply negative exponent rule

$8^{-8} = \frac{1}{8^8}$

Step3: Rewrite $8^8$ as repeated multiplication

$\frac{1}{8^8} = \frac{1}{8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8}$

Answer:

$\frac{1}{8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8}$ (the fourth option)