Question

select all the expressions that are equivalent to $11^{4} \cdot 11^{8}$.$\frac{1}{11^{12}}$$11^{12}$$(11^{9})^{3}$$\frac{1}{11^{32}}$

Explanation:

Step1: Apply exponent product rule

When multiplying exponents with the same base, add the exponents: $a^m \cdot a^n = a^{m+n}$.
For $11^4 \cdot 11^8$, we calculate:
$11^{4+8} = 11^{12}$

Step2: Evaluate each option

• Option 1: $\frac{1}{11^{12}} = 11^{-12}$, which is not equal to $11^{12}$.
• Option 2: $11^{12}$, which matches the result from Step1.
• Option 3: $(11^9)^3 = 11^{9 \times 3} = 11^{27}$, which is not equal to $11^{12}$.
• Option 4: $\frac{1}{11^{32}} = 11^{-32}$, which is not equal to $11^{12}$.

Answer:

$11^{12}$