Solve (3×6)/5 Raised to the Negative Fourth Power: Complete Solution

Insert the corresponding expression:

$\left(\frac{3\times6}{5}\right)^{-4}=$

To solve this problem, let's break down the expression and apply the rules of exponents:

Step-by-Step Solution:

• Step 1: Understand that the expression given is $\left(\frac{3 \times 6}{5}\right)^{-4}$.
• Step 2: Simplify the fraction $\frac{3 \times 6}{5}$ as a single fraction, which is already given.
• Step 3: Use the property of negative exponents: $\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^{n}$. This lets us convert the expression.
• Step 4: Apply the negative exponent $-4$ to each component inside the fraction: $(3 \times 6)^{-4}$ becomes $3^{-4} \times 6^{-4}$ and the denominator $5^{-4}$.

Combining these steps results in the expression:

$\frac{3^{-4} \times 6^{-4}}{5^{-4}}$

This matches choice 3, which is the correct answer.

Therefore, the solution to the problem is $\frac{3^{-4} \times 6^{-4}}{5^{-4}}$.