Solve (5×11)/(3×7) Raised to Power a: Complex Fraction Expression

Insert the corresponding expression:

$\left(\frac{5\times11}{3\times7}\right)^a=$

To solve this problem, follow these steps:

• Identify the given expression: $\left(\frac{5 \times 11}{3 \times 7}\right)^a$.

• Apply the exponent rule for powers of a fraction: $\left(\frac{x}{y}\right)^a = \frac{x^a}{y^a}$.

• Apply this rule separately to the numerator and the denominator:

The numerator is $5 \times 11$ and the denominator is $3 \times 7$. When the fraction is raised to a power $a$, we apply the power to both the numerator and denominator:

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

Which corresponds to option 1.

Each product is raised to the power $a$. By exponent rules $(xy)^a = x^a \times y^a$, this expression becomes:

$\frac{5^a \times 11^a}{3^a \times 7^a}$

Thus, the expression can be rewritten as: $\frac{5^a \times 11^a}{3^a \times 7^a}$.

Referring to the provided choices, this matches choice 3.

Therefore, the correct choice is 4, A+C are correct.