Solve Exponential Expression: 5^8 × 8^8 × 10^8 Multiplication

The goal is to apply the power of a product rule by transforming the expression $5^8 \times 8^8 \times 10^8$ into the form $(a \times b \times c)^n$.

Let's begin by identifying the terms involved:

• The expression consists of three separate terms, each raised to the 8th power: $5^8$, $8^8$, and $10^8$.

According to the power of a product rule, $(a \times b \times c)^n = a^n \times b^n \times c^n$. Therefore, given that the exponents are the same ($n = 8$), we can reverse this process.

• The original expression is $5^8 \times 8^8 \times 10^8$.

We can then consolidate this into a single term by combining the bases under the same exponent:

Thus, $5^8 \times 8^8 \times 10^8 = (5 \times 8 \times 10)^8$.

Therefore, the corresponding expression is:

$\left(5\times8\times10\right)^8$