Question

which expression is equivalent to $(12^{4})(12^{-9})$a. $12^{-36}$b. $-12^{5}$c. $\frac{1}{12^{5}}$d. $\frac{1}{12^{-5}}$

Explanation:

Step1: Apply exponent product rule

When multiplying terms with the same base, add exponents: $a^m \times a^n = a^{m+n}$.
For $(12^4)(12^{-9})$, this gives $12^{4 + (-9)} = 12^{-5}$.

Step2: Rewrite negative exponent

A term with a negative exponent can be rewritten as a reciprocal: $a^{-k} = \frac{1}{a^k}$.
So $12^{-5} = \frac{1}{12^5}$.

Answer:

C. $\frac{1}{12^5}$