Certainly! Below are the guided notes for Unit 3 on Exponents and Scientific Notation, including vocabulary key terms, meanings, and examples.
Unit 3 Exponents and Scientific Notation Guided Notes
Vocabulary
| Key Terms | Meaning | Example | |------------------------------------------------|---------------------------------------------------------------------------------------------------|-------------------------------| | Standard Form | The usual way of writing numbers (not in scientific notation). | 1,000 or 3,500 | | Base | The number that is being multiplied in an exponent. | In \(3^4\), 3 is the base. | | Exponent | Indicates how many times the base is multiplied by itself. | In \(3^4\), 4 is the exponent. | | Multiplying like bases Rule | When multiplying two numbers with the same base, add the exponents. | \(a^m \cdot a^n = a^{m+n}\) | | Dividing like bases Rule | When dividing two numbers with the same base, subtract the exponents. | \(a^m / a^n = a^{m-n}\) | | Zero Power Rule | Any non-zero number raised to the power of zero is equal to one. | \(5^0 = 1\) | | Power to a Power Rule | When raising a power to another power, multiply the exponents. | \((a^m)^n = a^{m \cdot n}\) | | When there are parentheses, what gets the power? | The exponent applies to everything inside the parentheses. | \((a \cdot b)^n = a^n \cdot b^n\) | | Negative Integer Exponent Rule | A negative exponent represents the reciprocal of the base raised to the opposite positive exponent.| \(a^{-n} = \frac{1}{a^n}\) | | Compare \(10^2\) to \(10^{-2}\) | \(10^2 = 100\) while \(10^{-2} = \frac{1}{10^2} = \frac{1}{100} = 0.01\) | | Put all Exponent Rules Picture here | [Include a visual representation of all exponent rules here if required. Adjust it based on your needs.] |
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