Power of a Product Property

Suppose \(a\) and \(b\) are nonzero real numbers and \(x\) and \(y\) are any integers,

$$\large{{\left( {a \cdot b} \right)^x} = {a^x} \cdot {b^x}}$$

Description: To determine the power of a product, apply the exponent to each individual factor. This involves distributing the outer exponent to the exponent of each factor.

Some examples:

$${\left( {5 \cdot 7} \right)^5} = {5^5} \cdot {7^5}$$

$${\left( {{2^x} \cdot {3^y}} \right)^2} = {2^{2x}} \cdot {3^{2y}}$$