You probably learned (and then forgot) these identities in middle school or high school: \begin{aligned} \left(x^{a}\right)\left(x^{b}\right) &=x^{a+b} \\ \left(x^{a}\right)^{b} &=x^{a b} \\ \log _{x}(a b) &=\log _{x} a+\log _{x} b \\ a \log _{x} b &=\log _{x}\left(b^{a}\right) \end{aligned} Well, it’s time to get reacquainted with them again.
In particular, never ever write $$\left(x^{a}\right)\left(x^{b}\right)=x^{a b}$$. If you write this, your cryptography instructor will realize that life is too short, immediately resign from teaching, and join a traveling circus. But not before changing your grade in the course to a zero.