Calculate (8×5×2)^7: Evaluating the Seventh Power of a Product

The problem involves applying the power of a product rule in exponents. This rule states that when you raise a product to an exponent, you can apply the exponent to each factor in the product separately. Mathematically, this rule is expressed as: $(a \times b \times c)^n = a^n \times b^n \times c^n$.

We need to apply the power of a product rule to our expression.

First, identify each individual factor in the product:

• Factor 1: $8$

• Factor 2: $5$

• Factor 3: $2$

Now, apply the exponent $7$ to each factor:

• $8^7$

• $5^7$

• $2^7$

Therefore, the expression $(8 \times 5 \times 2)^7$ simplifies to:

$8^7 \times 5^7 \times 2^7$