Podcast
Questions and Answers
What happens when the same bases are divided?
What happens when the same bases are divided?
What is the result of any base with a zero exponent?
What is the result of any base with a zero exponent?
What happens when a base with an exponent is raised to another power?
What happens when a base with an exponent is raised to another power?
What happens to the negative sign when a base with a negative exponent is moved to the opposite side of the fraction?
What happens to the negative sign when a base with a negative exponent is moved to the opposite side of the fraction?
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What is the rule for handling negative bases?
What is the rule for handling negative bases?
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What happens when a base 'a' is multiplied by itself 'n' number of times?
What happens when a base 'a' is multiplied by itself 'n' number of times?
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How are the exponents treated when the same bases are multiplied?
How are the exponents treated when the same bases are multiplied?
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What is the result when a base has an exponent of zero?
What is the result when a base has an exponent of zero?
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What happens to a negative base when it is enclosed in parentheses?
What happens to a negative base when it is enclosed in parentheses?
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How are the exponents treated when the same bases are raised to a power?
How are the exponents treated when the same bases are raised to a power?
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Study Notes
Powers
- Definition: When a base "a" is multiplied by itself "n" number of times
- Notation: a^n
Powers with Negative Bases
- Rule: When a base is negative, the negative is included only if the base is enclosed in parentheses
- Example: -(a^n) vs (-a)^n
Zero Powers
- Rule: Any base with a zero exponent is equal to 1
- Example: a^0 = 1
Operations with Powers
- Base Times a Base: When the same bases are multiplied, the exponents are added
- Example: a^m × a^n = a^(m+n)
- Base Divided By a Base: When the same bases are divided, the exponents are subtracted
- Example: a^m ÷ a^n = a^(m-n)
Power to a Power
- Rule: When a base with an exponent is raised to another power, the exponents are multiplied
- Example: (a^m)^n = a^(m×n)
Negative Exponents
- Rule: When a base has a negative exponent, the base and exponent are moved to the opposite side of the fraction
- Example: a^(-n) = 1/a^n
- Note: The negative sign is removed when the base is moved to the opposite side of the fraction
Powers
- Definition: When a base "a" is multiplied by itself "n" number of times
- Notation: a^n
Powers with Negative Bases
- Rule: When a base is negative, the negative is included only if the base is enclosed in parentheses
- Example: -(a^n) vs (-a)^n
Zero Powers
- Rule: Any base with a zero exponent is equal to 1
- Example: a^0 = 1
Operations with Powers
- Base Times a Base: When the same bases are multiplied, the exponents are added
- Example: a^m × a^n = a^(m+n)
- Base Divided By a Base: When the same bases are divided, the exponents are subtracted
- Example: a^m ÷ a^n = a^(m-n)
Power to a Power
- Rule: When a base with an exponent is raised to another power, the exponents are multiplied
- Example: (a^m)^n = a^(m×n)
Negative Exponents
- Rule: When a base has a negative exponent, the base and exponent are moved to the opposite side of the fraction
- Example: a^(-n) = 1/a^n
- Note: The negative sign is removed when the base is moved to the opposite side of the fraction
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Description
This quiz covers the rules of exponents, including powers with negative bases, zero powers, and power to a power. Learn about the different rules and properties of exponents.
