Simplify the Complex Fraction: (2⁴×3⁵)/(7⁴×11⁵)

To solve the problem, we will utilize the properties of exponents to express the given fraction properly.

The given expression is $\frac{2^4 \times 3^5}{7^4 \times 11^5}$. Our goal is to rewrite this expression using properties of exponents.

Let's break it down into two separate expressions based on the properties of division of exponents:

• $\frac{2^4}{7^4} = \left(\frac{2}{7}\right)^4$ because $\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m$.
• $\frac{3^5}{11^5} = \left(\frac{3}{11}\right)^5$ for the same reasons as above.

By rewriting the original expression using these properties, we have:

$\frac{2^4 \times 3^5}{7^4 \times 11^5} = \left(\frac{2}{7}\right)^4 \times \left(\frac{3}{11}\right)^5$.

Therefore, the expression can be rewritten as $\left(\frac{2}{7}\right)^4 \times \left(\frac{3}{11}\right)^5$. This corresponds to choice 3 in the provided options.

The correct transformation of the expression is effectively represented and confirmed with the properties of exponents.