Question

select all the expressions that are equivalent to $12^{-4} \cdot 12^{2}$.
$\frac{12^{-5}}{12^{-3}}$
$\frac{12^{-8}}{12}$
$12^{-8}$
$12^{-2}$

Explanation:

Step1: Simplify the original expression

When multiplying exponents with the same base, add the exponents:
$12^{-4} \cdot 12^{2} = 12^{-4+2} = 12^{-2}$

Step2: Simplify first option

When dividing exponents with the same base, subtract the exponents:
$\frac{12^{-5}}{12^{-3}} = 12^{-5-(-3)} = 12^{-5+3} = 12^{-2}$

Step3: Simplify second option

$\frac{12^{-8}}{12} = 12^{-8-1} = 12^{-9}$

Step4: Simplify third option

$12^{-8}$ is already in simplest form, which is not equal to $12^{-2}$

Step5: Simplify fourth option

$12^{-2}$ is already in simplest form, matching the original expression's simplified form.

Answer:

• $\frac{12^{-5}}{12^{-3}}$
• $12^{-2}$