Question

4 select all that are equivalent to $8^{-2}$
a $\frac{1}{64}$
b $-8^2$
c $-64$
d $\frac{1}{8^2}$
e $-\frac{1}{64}$

Explanation:

Step1: Recall the negative exponent rule

The rule for negative exponents is \( a^{-n}=\frac{1}{a^{n}} \) (where \( a
eq0 \) and \( n \) is a positive integer). For \( 8^{-2} \), applying this rule, we get \( 8^{-2}=\frac{1}{8^{2}} \).

Step2: Calculate \( 8^{2} \)

We know that \( 8^{2}=8\times8 = 64 \). So \( \frac{1}{8^{2}}=\frac{1}{64} \).

Step3: Analyze other options

• Option B: \( - 8^{2}=- (8\times8)=-64 \), which is not equal to \( 8^{-2} \).
• Option C: \( - 64\) is the value of \( - 8^{2} \), not equal to \( 8^{-2} \).
• Option E: \( -\frac{1}{64}\) has a negative sign, while \( 8^{-2}=\frac{1}{64} \) is positive, so they are not equal.

Answer:

A. \(\frac{1}{64}\), D. \(\frac{1}{8^{2}}\)