Mathematic power of multiplication

The power of a product is the rule that raising a product of two or more factors to an exponent gives the same result as raising each factor to that exponent separately and then multiplying the outcomes. In other words, an exponent placed on a bracket that contains a multiplication distributes onto every factor inside it. This works because a power is just repeated multiplication, so the shared factors can be regrouped without changing the total.

The rule holds for any number of factors, for positive, negative, and fractional exponents, and even for variables, which makes it a cornerstone of the laws of exponents. It also runs both ways: you can expand a bracketed product or, in reverse, pull a common exponent back into brackets to simplify an expression. In practice it lets you rewrite awkward products, factor terms, and simplify roots, since a root is just a fractional power. That is why it turns up constantly in algebra, scientific notation, and physics formulas, where breaking a power apart or joining factors together makes calculations far cleaner.