Question

which expression is equivalent to $6^{6} \cdot 10^{6}$?
$60^{12}$ $60^{36}$ $\frac{1}{60^{-6}}$ $\frac{1}{60^{6}}$

Explanation:

Step1: Apply exponent product rule

Recall the rule $a^n \cdot b^n = (a \cdot b)^n$. Here $a=6$, $b=10$, $n=6$.
$6^6 \cdot 10^6 = (6 \times 10)^6 = 60^6$

Step2: Simplify negative exponent option

Use the rule $\frac{1}{x^{-k}} = x^k$. For $\frac{1}{60^{-6}}$, this equals $60^6$.

Answer:

C. $\frac{1}{60^{-6}}$