The laws of exponents, or laws of indices, or even power laws are all the rules we have to know on order to do operations with numbers raised to a power.
In this section we learn the rules for all the basic operations we need to know how to do with powers of numbers:
No simplication can be made when adding, or subtracting, two exponentials.
In mathematical terms that's
\[a^m + a^n = a^m + a^n\]
\[ a^m \times a^n = a^{m+n}\]
\[a^m\times b^n = a^m \times b^n\]
No simplication can be made.
exception
If exponents are equal \(m=n\)
\[a^m\times b^m = \begin{pmatrix}a\times b \end{pmatrix}^m\]
\(3^2\times 3^5 = 3^{2+5} = 3^7\)