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Study Guides > College Algebra

Key Concepts & Glossary

Key Equations

Rules of Exponents For nonzero real numbers aa and bb and integers mm and nn
Product rule aman=am+n{a}^{m}\cdot {a}^{n}={a}^{m+n}
Quotient rule aman=amn\frac{{a}^{m}}{{a}^{n}}={a}^{m-n}
Power rule (am)n=amn{\left({a}^{m}\right)}^{n}={a}^{m\cdot n}
Zero exponent rule a0=1{a}^{0}=1
Negative rule an=1an{a}^{-n}=\frac{1}{{a}^{n}}
Power of a product rule (ab)n=anbn{\left(a\cdot b\right)}^{n}={a}^{n}\cdot {b}^{n}
Power of a quotient rule (ab)n=anbn{\left(\frac{a}{b}\right)}^{n}=\frac{{a}^{n}}{{b}^{n}}

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 a×10na\times {10}^{n} where 1a<101\le |a|<10 and nn is an integer  

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  • College Algebra. Provided by: OpenStax Authored by: OpenStax College Algebra. Located at: https://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1/Preface. License: CC BY: Attribution.