Sometimes, you want to raise an exponential expression itself to a power. For example, you might want to compute (−2x2)2. For this, you need two more rules. First, if you're raising a bunch of things multiplied together to a power, you can distribute the power so it applies to each thing individually. For example, (−2x2)3 = (−2)3(x2)3. (Of course, this rule works for division as well as multiplication.) To finish this problem, we need to know what (−2)3 and (x2)3 are. I hope you already know (−2)2 is −8. For (x2)3, we need the second rule, which says that if a power is raised to another power, you multiply the exponents. This means that (x2)3 = x6, so our answer is −8x6.
Don't get this rule confused with the one in the last section! Remember, if you're multiplying two exponentials, then the exponents add. If you're raising one exponential to a power, then the exponents multiply.