Evaluate (5×2×6×3)^7: Product and Power Expression

To solve this problem, we'll convert the given product inside the parentheses, $\left(5 \times 2 \times 6 \times 3\right)^7$, into an expression applying the power of a product rule.

First, recognize that we can apply the rule of exponents as follows:

• The power of a product rule states $(a \times b)^n = a^n \times b^n$.

Applying this to our variables, we have:

• $\left(5 \times 2 \times 6 \times 3\right)^7 = (5)^7 \times (2)^7 \times (6)^7 \times (3)^7$

Therefore, the expression evaluates to:

$5^7 \times 2^7 \times 6^7 \times 3^7$