Solve (3×7)/(4×6) Raised to Power -6: Negative Exponent Practice

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

• Step 1: Apply the negative exponent rule.
• Step 2: Use the power of a fraction rule to simplify the expression.
• Step 3: Ensure calculations are conducted correctly, and choose the matching answer from the choices.

Now, let's work through each step:
Step 1: The initial expression is $\left(\frac{3 \times 7}{4 \times 6}\right)^{-6}$. First, use the negative exponent rule: $\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^{n}$. So, the expression becomes $\left(\frac{4 \times 6}{3 \times 7}\right)^{6}$.

Step 2: Apply the power of a fraction rule: $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$. Thus, the expression can be re-written as:

$\frac{(4 \times 6)^6}{(3 \times 7)^6}$

Step 3: Assess the provided answer choices and determine which one matches our derived expression. Choice 3, $\frac{(4 \times 6)^6}{(3 \times 7)^6}$, correctly corresponds to our simplified result.

Therefore, the solution to the problem is $\frac{(4 \times 6)^6}{(3 \times 7)^6}$, which corresponds to choice 3.