10 Questions
What happens when the same bases are divided?
The exponents are subtracted
What is the result of any base with a zero exponent?
The result is 1
What happens when a base with an exponent is raised to another power?
The exponents are multiplied
What happens to the negative sign when a base with a negative exponent is moved to the opposite side of the fraction?
The negative sign is removed
What is the rule for handling negative bases?
The negative is included only if the base is enclosed in parentheses
What happens when a base 'a' is multiplied by itself 'n' number of times?
The base is raised to the power of 'n'
How are the exponents treated when the same bases are multiplied?
The exponents are added
What is the result when a base has an exponent of zero?
The result is always one
What happens to a negative base when it is enclosed in parentheses?
The negative sign is included
How are the exponents treated when the same bases are raised to a power?
The exponents are multiplied
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
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.
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