Certainly! Here are the key terms along with their meanings and examples:
U3 L1
Standard Form
- Meaning: A way of writing numbers using digits, typically in a format that is easy to read such as integers, decimals, or fractions.
- Example: The standard form of the number "seven thousand eight hundred twenty-three" is written as 7,823.
Base
- Meaning: The number that is multiplied by itself when raised to an exponent.
- Example: In \( 5^3 \), the base is 5.
Exponent
- Meaning: A number that indicates how many times the base is used as a factor.
- Example: In \( 4^2 \), the exponent is 2, which means \( 4 \times 4 \).
U3 L2
Multiplying Like Bases Rule
- Meaning: When multiplying numbers with the same base, add their exponents.
- Example: \( a^m \times a^n = a^{m+n} \) (e.g., \( 2^3 \times 2^2 = 2^{3+2} = 2^5 \)).
U3 L3
Dividing Like Bases Rule
- Meaning: When dividing numbers with the same base, subtract the exponent of the denominator from the exponent of the numerator.
- Example: \( \frac{a^m}{a^n} = a^{m-n} \) (e.g., \( \frac{5^4}{5^2} = 5^{4-2} = 5^2 \)).
U3 L4
Zero Power Rule
- Meaning: Any non-zero number raised to the power of zero is equal to one.
- Example: \( 7^0 = 1 \).
U3 L5
Power to a Power Rule
- Meaning: When exponentiating an exponent, multiply the exponents.
- Example: \( (a^m)^n = a^{mn} \) (e.g., \( (3^2)^3 = 3^{2 \times 3} = 3^6 \)).
U3 L5 (Continued)
When there are parentheses, how do you know what gets the power?
- Meaning: Inside parentheses, only the base and any factors immediately touching the parenthesis are raised to the power; distribute the exponent to every factor inside the parentheses.
- Example: \( (ab)^2 = a^2b^2 \).
U3 L6
Negative Integer Exponent Rule
- Meaning: A negative exponent represents the reciprocal of the base raised to the positive exponent.
- Example: \( a^{-n} = \frac{1}{a^n} \) (e.g., \( 2^{-3} = \frac{1}{2^3} = \frac{1}{8} \)).
U3 L6 (Continued)
Compare \( 10^2 \) to \( 10^{-2} \)
- Meaning: \( 10^2 = 100 \) represents a positive exponent, while \( 10^{-2} = \frac{1}{10^2} = \frac{1}{100} = 0.01 \) represents a negative exponent. The negative exponent results in a smaller value.
- Example: Thus, \( 10^2 (100) > 10^{-2} (0.01) \).
U3 L7
Put all Exponent Rules Picture here
- Meaning: This section typically would include visual summaries or charts illustrating the different exponent rules. You can create a visual chart or table that neatly outlines all the rules mentioned, which can serve as a quick reference for studying these concepts.
Feel free to ask if you need further explanations or examples!