Solve (10×3)/(7×9) Raised to Negative Fourth Power

To solve the problem, let's follow these steps:

• Step 1: Recognize that the given expression is $\left(\frac{10 \times 3}{7 \times 9}\right)^{-4}$. A negative exponent indicates that we should take the reciprocal of the base.
• Step 2: Rewrite this expression using the negative exponent rule: $\left(\frac{10 \times 3}{7 \times 9}\right)^{-4} = \left(\frac{7 \times 9}{10 \times 3}\right)^{4}$ This step inverts the fraction and changes the exponent from $-4$ to $4$.
• Step 3: Apply the exponent to each component of the fraction: $\left(\frac{7 \times 9}{10 \times 3}\right)^{4} = \frac{(7 \times 9)^{4}}{(10 \times 3)^{4}}$ This separates the powers between the numerator and the denominator.
• Step 4: Distribute the powers inside each product: $= \frac{7^4 \times 9^4}{10^4 \times 3^4}$ This is achieved by applying $(ab)^n = a^n \times b^n$ to both the numerator and the denominator.

Therefore, the simplified expression is $\frac{7^4 \times 9^4}{10^4 \times 3^4}$, which corresponds to choice 3 in the provided answer choices.