## Key Concepts

**Exponential Notation**

This is read \(a\) to the \({m}^{\mathrm{th}}\) power.

**Product Property of Exponents**- If \(a\) is a real number and \(m,n\) are counting numbers, then\({a}^{m}·{a}^{n}={a}^{m+n}\)
- To multiply with like bases, add the exponents.

- If \(a\) is a real number and \(m,n\) are counting numbers, then
**Power Property for Exponents**- If \(a\) is a real number and \(m,n\) are counting numbers, then(am)n=am⋅n(am)n=am⋅n

- If \(a\) is a real number and \(m,n\) are counting numbers, then
**Product to a Power Property for Exponents**- If \(a\) and \(b\) are real numbers and \(m\) is a whole number, then\({\left(ab\right)}^{m}={a}^{m}{b}^{m}\)

- If \(a\) and \(b\) are real numbers and \(m\) is a whole number, then