Question

evaluate. write your answer as a whole number or as a
$8^{-2} \cdot 11^{-2} = \frac{\square|\square}{\square}$

Explanation:

Step1: Recall negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\). So we can rewrite each term:
\(8^{-2}=\frac{1}{8^{2}}\) and \(11^{-2}=\frac{1}{11^{2}}\)

Step2: Multiply the two fractions

When multiplying fractions \(\frac{1}{8^{2}}\cdot\frac{1}{11^{2}}\), we multiply the numerators and the denominators. The numerator is \(1\times1 = 1\). The denominator is \(8^{2}\times11^{2}\).

Step3: Calculate \(8^{2}\) and \(11^{2}\)

\(8^{2}=8\times8 = 64\) and \(11^{2}=11\times11 = 121\)

Step4: Multiply the denominators

Now we multiply \(64\times121\). Let's calculate that: \(64\times121=(60 + 4)\times121=60\times121+4\times121=7260+484 = 7744\)
So the fraction is \(\frac{1}{7744}\)

Answer:

\(\frac{1}{7744}\)