Simplify (11×8)⁴ ÷ (11×8)¹¹: Laws of Exponents Practice

Insert the corresponding expression:

$\frac{\left(11\times8\right)^4}{\left(11\times8\right)^{11}}=$

To solve this problem, we'll follow these steps:

• Step 1: Apply the quotient rule for exponents
• Step 2: Simplify the exponent
• Step 3: Interpret the negative exponent
• Step 4: Match with the given choices

Let's walk through each step:

Step 1: The quotient rule for exponents states that $\frac{a^m}{a^n} = a^{m-n}$. Here, both the numerator and the denominator are powers with the same base, $11 \times 8$.

Step 2: Apply the rule: $\frac{(11 \times 8)^4}{(11 \times 8)^{11}} = (11 \times 8)^{4 - 11} = (11 \times 8)^{-7}$.

Step 3: The negative exponent $-7$ indicates the reciprocal of the base raised to the positive exponent. Therefore, $(11 \times 8)^{-7} = \frac{1}{(11 \times 8)^7}$.

Step 4: Check the given answer choices:

• Choice 1: $(11\times8)^7$ is incorrect since it does not match our result of the reciprocal.
• Choice 2: $(11\times8)^{-7}$ is correct as it directly matches the simplified expression.
• Choice 3: $\frac{1}{(11\times8)^7}$ is also correct, as it represents the expression with a negative exponent as a fraction.
• Choice 4: "B+C are correct" matches our findings because both choices 2 and 3 are correct representations.

Therefore, the solution to the problem is the choice that states B+C are correct.