Question

question
which expression is equivalent to $6^{-1} \times 6^{-1}$?

answer
\\(\circ\\) 6 \\(\circ\\) 36
\\(\circ\\) \\(\frac{1}{36}\\) \\(\circ\\) 1

Explanation:

Step1: Apply exponent product rule

When multiplying terms with the same base, add exponents: $a^m \times a^n = a^{m+n}$.
$6^{-1} \times 6^{-1} = 6^{-1 + (-1)} = 6^{-2}$

Step2: Rewrite negative exponent

A negative exponent means reciprocal: $a^{-n} = \frac{1}{a^n}$.
$6^{-2} = \frac{1}{6^2}$

Step3: Calculate the denominator

$6^2 = 6 \times 6 = 36$, so $\frac{1}{6^2} = \frac{1}{36}$

Answer:

$\frac{1}{36}$ (the third option)