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Questions and Answers
What is the result of (3^2 × 3^4)?
What is the value of (2 × 3)^2?
What is the result of 2^5 ÷ 2^2?
What is the value of (3^2)^3?
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What is the value of a^0?
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Study Notes
Laws of Exponents
Product of Powers
- When multiplying two or more exponential expressions with the same base, add the exponents:
- a^m × a^n = a^(m + n)
- Example: 2^3 × 2^4 = 2^(3 + 4) = 2^7
Power of a Product
- When raising a product to a power, raise each factor to that power:
- (ab)^m = a^m × b^m
- Example: (2 × 3)^2 = 2^2 × 3^2 = 4 × 9 = 36
Quotient of Powers
- When dividing two exponential expressions with the same base, subtract the exponents:
- a^m ÷ a^n = a^(m - n)
- Example: 2^5 ÷ 2^3 = 2^(5 - 3) = 2^2
Power of a Power
- When raising an exponential expression to a power, multiply the exponents:
- (a^m)^n = a^(m × n)
- Example: (2^3)^2 = 2^(3 × 2) = 2^6
Zero Exponent Rule
- Any nonzero number raised to the power of 0 is equal to 1:
- a^0 = 1 (where a ≠0)
- Example: 2^0 = 1
Laws of Exponents
Product of Powers
- Multiplying exponential expressions with the same base involves adding the exponents.
- Formula: a^m × a^n = a^(m + n)
- Example: 2^3 × 2^4 = 2^(3 + 4) = 2^7
Power of a Product
- Raising a product to a power involves raising each factor to that power.
- Formula: (ab)^m = a^m × b^m
- Example: (2 × 3)^2 = 2^2 × 3^2 = 4 × 9 = 36
Quotient of Powers
- Dividing exponential expressions with the same base involves subtracting the exponents.
- Formula: a^m ÷ a^n = a^(m - n)
- Example: 2^5 ÷ 2^3 = 2^(5 - 3) = 2^2
Power of a Power
- Raising an exponential expression to a power involves multiplying the exponents.
- Formula: (a^m)^n = a^(m × n)
- Example: (2^3)^2 = 2^(3 × 2) = 2^6
Zero Exponent Rule
- Any nonzero number raised to the power of 0 is equal to 1.
- Formula: a^0 = 1 (where a ≠0)
- Example: 2^0 = 1
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Description
Learn about the rules of exponents, including product of powers, power of a product, and quotient of powers. Practice examples and exercises to understand the concepts.
