Solve (11×9/4)^-5: Negative Exponent Calculation

To solve this problem, let's begin by applying the mathematical rules for negative exponents and exponents of a fraction.

Step 1: Apply the negative exponent rule:

• Given: $\left(\frac{11 \times 9}{4}\right)^{-5}$.

• Using the rule $(a/b)^{-n} = (b/a)^n$, we rewrite this as $\left(\frac{4}{11 \times 9}\right)^5$.

Step 2: Simplify the expression:

• Analyzing the expression $\left(\frac{4}{11 \times 9}\right)^5$, we see that this is equivalent to:

• $\frac{4^5}{(11 \times 9)^5}$.

• Notice that $(11 \times 9)^5$ can also be written as $11^5 \times 9^5$ using properties of exponents.

• Thus, $\frac{4^5}{11^5 \times 9^5}$ is another way to express this fraction.

Step 3: Compare with given choices:

• Choice 2: $\frac{4^5}{11^5 \times 9^5}$ matches our final expression.

• Notice also Choice 3: $\frac{4^5}{(11 \times 9)^5}$ matches the form before simplifying the denominator completely to separate power terms.

Therefore, after comparison, Options B and C are indeed correct and thus the correct response is: B+C are correct.