Question

which expression is equivalent to $6 \cdot 6^{-2}$?
answer
$\circ$ 6 $\circ$ $\frac{1}{36}$
$\circ$ 36 $\circ$ $\frac{1}{6}$

Explanation:

Step1: Apply exponent addition rule

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

Step2: Simplify the exponent

Calculate the sum of the exponents:
$6^{1 - 2} = 6^{-1}$

Step3: Rewrite negative exponent

A negative exponent means the reciprocal: $a^{-k} = \frac{1}{a^k}$, so:
$6^{-1} = \frac{1}{6^1} = \frac{1}{6}$

Answer:

$\frac{1}{6}$ (corresponding to the option: $\frac{1}{6}$)