Equations Involving Exponential Expressions

Exponential expressions have two basic parts: exponent and base. The simplest equations involve one or the other.

1. If 2^{300} x 2^{n} = 2^{501} what is n?

2. If 2^{100} x 3^{100} = a^{100} what is a?

3. If 100^{n} x 5^{3} = 20^{n} x 5^{63} what is n?

4. If 2^{49} x 2^{n} = 1/4, what is n?

5. If (2^{n})^{10} = 32^{6} what is n?