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Study Guides > Prealgebra

Summary: Simplifying Expressions With Exponents

 

Key Concepts

  • Exponential Notation

On the left side, a raised to the m is shown. The m is labeled in blue as an exponent. The a is labeled in red as the base. On the right, it says a to the m means multiply m factors of a. Below this, it says a to the m equals a times a times a times a, with m factors written below in blue. This is read [latex]a[/latex] to the [latex]{m}^{\mathrm{th}}[/latex] power.

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

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