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

Choose the expression that corresponds to the following:

$\left(8\times7\times3\right)^8=$

To solve the expression $\left(8\times7\times3\right)^8$, we can use the power of a product rule. This rule states that when raising a product to an exponent, you can apply the exponent to each factor within the parentheses.

So, according to the rule:

$\left(8\times7\times3\right)^8 = 8^8 \times 7^8 \times 3^8$

Each of the factors: 8, 7, and 3 is independently raised to the power of 8.

This approach allows us to separate the original power into the power of each individual factor, making the expression equivalent to multiplying each of these results together.

Therefore, the corresponding expression that equals $\left(8\times7\times3\right)^8$ is:

• $8^8 \times 7^8 \times 3^8$

• Each factor separately raised to the 8th power, then multiplied together.

All answers similar to this transformation are correct, as they apply the correct exponent rules.