For each statement below enter a T (true) the statement is true and an F (false) otherwise. In this problem you need to get everything correct before receiving credit. Whenever there is a division below, we assume that the divisor is non-zero. We also assume that where it matters the base of any power is positive.
For all real numbers $a$, $b$, and $c$ $$a^ba^c = a^{bc}.$$
For all real numbers $a$, $b$, and $c$ $$a^ba^c = a^{b+c}.$$
For all real numbers $a$ and $b$ $$a^{-b} = \frac{1}{a^b}.$$
For all real numbers $a$ and $b$ $$a^{-b} = -a^b.$$
For all real numbers $a$ and $b$ $$a^{b} = ab.$$