Calculate (3×7×9)^8: Evaluating Product Raised to Power of 8

To solve the problem, we need to apply the rule of exponents known as the "power of a product." This rule states that when you raise a product to a power, you can distribute the exponent to each factor in the product.

Let's break it down with the given problem:

We have the expression $\left(3\times7\times9\right)^8$. According to the power of a product rule, this expression can be rewritten by raising each individual factor inside the parentheses to the power of 8:

• Take the number 3 and raise it to the power of 8: $3^8$
• Take the number 7 and raise it to the power of 8: $7^8$
• Take the number 9 and raise it to the power of 8: $9^8$

Now, we can use the rule to rewrite the original expression as the product of these terms:

$3^8\times7^8\times9^8$

This is the expression you obtain when you apply the power of a product rule to $\left(3\times7\times9\right)^8$.