Question

evaluate. write your answer as a whole number or as a simplified fraction. $\frac{12^{-6}}{12^{-5}} = \frac{}{}$

Explanation:

Step1: Apply exponent quotient rule

When dividing terms with the same base, subtract exponents: $\frac{a^m}{a^n}=a^{m-n}$
$\frac{12^{-6}}{12^{-5}}=12^{-6-(-5)}$

Step2: Simplify the exponent

Calculate the exponent value.
$12^{-6+5}=12^{-1}$

Step3: Rewrite negative exponent

A negative exponent means reciprocal: $a^{-k}=\frac{1}{a^k}$
$12^{-1}=\frac{1}{12}$

Answer:

$\frac{1}{12}$