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
    ${a}^{m}\cdot {a}^{n}={a}^{m+n}$
  • To multiply with like bases, add the exponents.
• Power Property for Exponents
  • If $a$ is a real number and $m,n$ are counting numbers, then
    ${\left({a}^{m}\right)}^{n}={a}^{m\cdot n}$
• Product to a Power Property for Exponents
  • If $a$ and $b$ are real numbers and $m$ is a whole number, then
    ${\left(ab\right)}^{m}={a}^{m}{b}^{m}$