Definition

If the base of the power is a product, as is the case with [[$ (4 \cdot 3)^2 $]]​, the expression is called a power of a product. These expressions be calculated using normal calculation rules: [[$ (4 \cdot 3)^2 = (12)^2 = 144 $]]. However, the power of a product also has its own calculation rules, which lead to the same result: [[$ (4 \cdot 3)^2 = 4^2 \cdot 3^2 = 16 \cdot 9 = 144 $]]​

The power of a product

The power of a product is a product of the power of the factors.

[[$ (a\cdot b)^n = a^n \cdot b^n $]].


The rule for calculating the power of a product does not necessarily have to be used when calculating with numerical values alone. However, expressions that include variables cannot be simplified according to normal calculation rules.