Evaluate (3×5×7)/(4×8×10) Raised to the Fifth Power

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

• Step 1: Identify the expression $\left(\frac{3 \times 5 \times 7}{4 \times 8 \times 10}\right)^5$.

• Step 2: Apply the rule for powers of fractions to simplify the expression.

• Step 3: Simplify the products and raise each factor to the power of 5.

Now, let's work through each step:
Step 1: The expression given is $\left(\frac{3 \times 5 \times 7}{4 \times 8 \times 10}\right)^5$.
Step 2: According to the power of a fraction rule, $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$, we can distribute the power of 5 to both the numerator and denominator:

$\left(\frac{3 \times 5 \times 7}{4 \times 8 \times 10}\right)^5 = \frac{(3 \times 5 \times 7)^5}{(4 \times 8 \times 10)^5}$

Step 3: Now apply the power to each factor:

$= \frac{3^5 \times 5^5 \times 7^5}{4^5 \times 8^5 \times 10^5}$

This matches the expression in choice 2. Therefore, the correct corresponding expression is $\frac{3^5 \times 5^5 \times 7^5}{4^5 \times 8^5 \times 10^5}$ and also $\frac{(3 \times 5 \times 7)^5}{(4 \times 8 \times 10)^5}$.

Therefore, the solution to the problem is A+B.