Question

5 which of the following expression is equivalent to $6^{-7}$? a $(-6)^{-7}$ b $\frac{1}{6^{7}}$ c $\frac{1}{(-6)^{-7}}$ d $\frac{1}{6^{-7}}$

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.

Step2: Apply the rule to \( 6^{-7} \)

Using the negative exponent rule with \( a = 6 \) and \( n=7 \), we get \( 6^{-7}=\frac{1}{6^{7}} \).

Step3: Analyze other options

• Option A: \( (-6)^{-7}=\frac{1}{(-6)^{7}}=-\frac{1}{6^{7}}

eq6^{-7} \)

• Option C: \( \frac{1}{(-6)^{-7}}=(-6)^{7}=-6^{7}

eq6^{-7} \)

• Option D: \( \frac{1}{6^{-7}} = 6^{7}

eq6^{-7} \)

Answer:

B. \(\frac{1}{6^{7}}\)