Question

which expression is equivalent to \\(\frac{11^{-6}}{11^2}\\)? \\(11^{-4}\\) \\(\frac{1}{11^8}\\) \\(11^{-3}\\) \\(11^8\\)

Explanation:

Step1: Recall exponent rule for division

When dividing exponents with the same base \( a \), we use the rule \( \frac{a^m}{a^n}=a^{m - n} \). Here, the base \( a = 11 \), \( m=-6 \), and \( n = 2 \).

Step2: Apply the exponent rule

Substitute the values into the rule: \( \frac{11^{-6}}{11^{2}}=11^{-6 - 2} \).

Step3: Simplify the exponent

Calculate \( -6-2=-8 \), so the expression becomes \( 11^{-8} \). Now, recall the negative exponent rule \( a^{-n}=\frac{1}{a^{n}} \), so \( 11^{-8}=\frac{1}{11^{8}} \).

Answer:

\(\frac{1}{11^{8}}\) (corresponding to the option with \(\frac{1}{11^{8}}\))