Simplify the Exponential Fraction: (5¹⁰ × 8¹⁰)/(4¹⁰ × 7¹⁰)

Insert the corresponding expression:

$$$\frac{5^{10}\times8^{10}}{4^{10}\times7^{10}}=$

To simplify the expression $\frac{5^{10}\times8^{10}}{4^{10}\times7^{10}}$, we start by applying the property of exponents: $(a \times b)^n = a^n \times b^n$.

Step 1: Rewrite the expression. Notice that both the numerator and the denominator consist of two numbers, each raised to the power of 10.

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

Now, we notice we can apply the equality for exponential simplification:

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

Concluding, the simplified expression of the given problem is equivalent to option "1":

The expression simplifies to $\frac{\left(5\times8\right)^{10}}{\left(4\times7\right)^{10}}$, which aligns perfectly with choice id="1".

Therefore, the final answer is:

$\frac{\left(5\times8\right)^{10}}{\left(4\times7\right)^{10}}$.