5: Exponents and Exponent Rules
- Page ID
- 45180
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)
- 5.1: Definition of aⁿ
- For any real number a and a positive number n , aⁿ is the repeated multiplication of a by itself n times.
- 5.2: The Product Rule for Exponents
- For any real number a and positive numbers m and n , the product rule for exponents is the following.
- 5.3: The Quotient Rule of Exponents
- For any real number a and positive numbers m and n , where m>n . The Quotient Rule For Exponents is the following.
- 5.4: Zero Exponent Rule
- In section 5.3, the exponent of the number in the numerator was always greater than the exponent of the number in the denominator. In section 5.4, the exponent of the number in the numerator will be equal to the exponent of the number in the denominator.
- 5.5: The Negative Exponent Rule
- In section 5.3, The exponent of the number in the numerator was greater than the exponent of the number in the denominator. In section 5.4, the exponent of the number in the numerator was equal to the exponent of the number in the denominator. In section 5.5, the exponent of the number in the denominator may be greater than the exponent of the number in the numerator.
- 5.6: Power Rule For Exponents
- This rule helps to simplify an exponential expression raised to a power. This rule is often confused with the product rule, so understanding this rule is important to successfully simplify exponential expressions.
- 5.7: The power of a product rule for exponents
- The power of a product rule for exponents will deal with expressions where a product of bases is raised to some power.
- 5.8: Power of a quotient rule for exponents
- The power of a quotient rule for exponents will focus on what happens to a quotient when it is raised to some power.
- 5.9: Rational Exponents
- Exponents are not always integers. This section will look into the cases where an exponent is a rational number. When an exponent is a rational number, the expression may be written as an expression with a radical. The rule is to write your answer in the same form as the original problem (if you start with exponents, end with exponents, or if you start with radicals, end with radicals).