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Study Guides > College Algebra CoRequisite Course

Summary: Review

Key Equations

Rules of Exponents For nonzero real numbers aa and bb and integers mm and nn
Product rule am⋅an=am+n{a}^{m}\cdot {a}^{n}={a}^{m+n}
Quotient rule aman=am−n\dfrac{{a}^{m}}{{a}^{n}}={a}^{m-n}
Power rule (am)n=am⋅n{\left({a}^{m}\right)}^{n}={a}^{m\cdot n}
Zero exponent rule a0=1{a}^{0}=1
Negative rule a−n=1an{a}^{-n}=\dfrac{1}{{a}^{n}}
Power of a product rule (a⋅b)n=an⋅bn{\left(a\cdot b\right)}^{n}={a}^{n}\cdot {b}^{n}
Power of a quotient rule (ab)n=anbn{\left(\dfrac{a}{b}\right)}^{n}=\dfrac{{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.
    • Corresponding input and output pairs of a function each represent a point on the graph of the function.
    • Each point contained on the graph of a function satisfies the equation of a function.

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