Sometimes, you want to raise an exponential
expression *itself* to a power. For example, you might want
to compute (−2*x*^{2})^{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,
(−2*x*^{2})^{3} =
(−2)^{3}(*x*^{2})^{3}. (Of
course, this rule works for division as well as multiplication.)
To finish this problem, we need to know what
(−2)^{3} and (*x*^{2})^{3} are.
I hope you already know (−2)^{2} is −8. For
(*x*^{2})^{3}, we need the second rule, which
says that if a power is raised to *another* power, you
multiply the exponents. This means that
(*x*^{2})^{3} = *x*^{6}, so our
answer is −8*x*^{6}.

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*.