Calculate (12×3)^5: Evaluating the Fifth Power of a Product

Choose the expression that corresponds to the following:

$\left(12\times3\right)^5=$

The given expression is $(12 \times 3)^5$. The power of a product rule states that $(a \times b)^n = a^n \times b^n$. We will apply this formula to the expression.

• Firstly, identify the base of the power as the product $12 \times 3$.

• Secondly, recognize that the exponent applied to this product is 5.

• According to the rule, the power of a product can be distributed to each factor in the product, which means: $(12 \times 3)^5 = 12^5 \times 3^5$.

Therefore, the expression $(12 \times 3)^5$ corresponds to $12^5 \times 3^5$.