Powers

Base: a Exponent: e

a^e = a_1 \cdot a_2 \cdot a_3 \cdot \dots \cdot a_e

Power Laws with same base

If you multiply two powers with the same base you can strip the base and just add up the exponents.

3^2 \cdot 3^5 = 3^{2+5} = 3^7

The same applies for division, but you have to subtract instead.

3^2 : 3^5 = 3^{2-5} = 3^{-3}

Exponents of a Exponent

If your exponent has an exponent you can flatten that expression by multiplying them.

a^{b^c} = a^{b \cdot c}

Power Laws with same exponent

If you multiply two powers with the same exponent you can calculate the product of those bases and then add the exponent.

3^2 \cdot 5^2 = (3 \cdot 5)^2 = 15^2

The same applies for division, but you calculate quotient.

4^2 : 2^2 = (4 : 2)^2 = 2^2