Summary: Exponents and Scientific Notation
Key Equations
Rules of Exponents For nonzero real numbers [latex]a[/latex] and [latex]b[/latex] and integers [latex]m[/latex] and [latex]n[/latex] | |
Product rule | [latex]{a}^{m}\cdot {a}^{n}={a}^{m+n}[/latex] |
Quotient rule | [latex]\frac{{a}^{m}}{{a}^{n}}={a}^{m-n}[/latex] |
Power rule | [latex]{\left({a}^{m}\right)}^{n}={a}^{m\cdot n}[/latex] |
Zero exponent rule | [latex]{a}^{0}=1[/latex] |
Negative rule | [latex]{a}^{-n}=\frac{1}{{a}^{n}}[/latex] |
Power of a product rule | [latex]{\left(a\cdot b\right)}^{n}={a}^{n}\cdot {b}^{n}[/latex] |
Power of a quotient rule | [latex]{\left(\frac{a}{b}\right)}^{n}=\frac{{a}^{n}}{{b}^{n}}[/latex] |
Key Concepts
- Products of exponential expressions with the same base can be simplified by adding exponents.
- Quotients of exponential expressions with the same base can be simplified by subtracting exponents.
- Powers of exponential expressions with the same base can be simplified by multiplying exponents.
- An expression with exponent zero is defined as 1.
- An expression with a negative exponent is defined as a reciprocal.
- The power of a product of factors is the same as the product of the powers of the same factors.
- The power of a quotient of factors is the same as the quotient of the powers of the same factors.
- The rules for exponential expressions can be combined to simplify more complicated expressions.
- Scientific notation uses powers of 10 to simplify very large or very small numbers.
- Scientific notation may be used to simplify calculations with very large or very small numbers.
Glossary
scientific notation a shorthand notation for writing very large or very small numbers in the form [latex]a\times {10}^{n}[/latex] where [latex]1\le |a|<10[/latex] and [latex]n[/latex] is an integerLicenses & Attributions
CC licensed content, Original
- Revision and Adaptation. Provided by: Lumen Learning License: CC BY: Attribution.
CC licensed content, Shared previously
- College Algebra. Provided by: OpenStax Authored by: Abramson, Jay et al.. License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].
CC licensed content, Specific attribution
- College Algebra. Provided by: OpenStax Authored by: OpenStax College Algebra. Located at: https://cnx.org/contents/[email protected]:1/Preface. License: CC BY: Attribution.