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] |
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| 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 integer