Simplify the Expression: 11^-2 × 11^-5 × 11^-4 Using Exponent Laws

Reduce the following equation:

$11^{-2}\times11^{-5}\times11^{-4}=$

To solve the expression $11^{-2} \times 11^{-5} \times 11^{-4}$, we apply the rules for multiplying numbers with the same base:

• Step 1: Use the rule for multiplying powers with the same base: $a^m \times a^n = a^{m+n}$.

• Step 2: Add the exponents: $-2 + -5 + -4$.

• Step 3: Perform the calculation: $-2 - 5 - 4 = -11$.

• Step 4: Write the expression with the combined exponent: $11^{-11}$.

• Step 5: Express $11^{-11}$ as a positive power using the property of negative exponents: $a^{-n} = \frac{1}{a^n}$.

Therefore, $11^{-11} = \frac{1}{11^{11}}$.

The final answer is $\frac{1}{11^{11}}$.