The Power Rule Basics
Ever wondered what happens when you raise a power to another power? That's exactly what the power rule helps us solve! When you have , you're actually multiplying by itself twice: . This expands to , which equals .
Looking at examples like and , a pattern emerges. In each case, when we expand and count all the factors, we find that the exponents multiply together. This gives us the power rule: . So for example, .
The power rule works with negative exponents too. For instance, , which can also be written as . When both exponents are negative, like in , they multiply to give a positive result: .
💡 If you ever forget the power rule, you can always go back to basics! Just write out the expression in expanded form and count how many times the base appears.
