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
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- 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.
Licenses & Attributions
CC licensed content, Original
- Provided by: Lumen Learning License: CC BY: Attribution.
