Summary: Review

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]\dfrac{{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}=\dfrac{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(\dfrac{a}{b}\right)}^{n}=\dfrac{{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.
    • 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.