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Questions and Answers
What does the exponent in the expression a^n represent?
What does the exponent in the expression a^n represent?
What is the result of (2^3)^2?
What is the result of (2^3)^2?
What is the value of a in the equation a^2 = 16?
What is the value of a in the equation a^2 = 16?
What is the result of (2 × 3)^2?
What is the result of (2 × 3)^2?
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What is the result of 2^3 × 2^5?
What is the result of 2^3 × 2^5?
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Study Notes
Exponents and Squared Numbers
Definition of Exponents
- Exponents are a shorthand way to represent repeated multiplication of a number by itself
- Expressed as
a^n, whereais the base andnis the exponent or power - The exponent indicates how many times the base is multiplied by itself
Squared Numbers
- A squared number is a number raised to the power of 2
- Expressed as
a^2, whereais the base - Example: 2 squared, or 2^2, is equivalent to 2 × 2 = 4
Properties of Exponents
-
Product of Powers:
a^m × a^n = a^(m+n) -
Power of a Product:
(ab)^n = a^n × b^n -
Power of a Power:
(a^m)^n = a^(mn)
Examples of Squared Numbers
- 3^2 = 3 × 3 = 9
- 4^2 = 4 × 4 = 16
- 5^2 = 5 × 5 = 25
Exponents and Squared Numbers
Definition of Exponents
- Exponents represent repeated multiplication of a number by itself in a concise way
- The notation
a^nrepresents the baseamultiplied by itselfntimes
Squared Numbers
- A squared number is a number raised to the power of 2, denoted as
a^2 - It is equivalent to multiplying the base
aby itself - For example, 2 squared, or 2^2, is equal to 2 × 2 = 4
Properties of Exponents
Product of Powers
- When multiplying two exponential expressions with the same base, add the exponents:
a^m × a^n = a^(m+n)
Power of a Product
- When raising a product to a power, raise each factor to that power:
(ab)^n = a^n × b^n
Power of a Power
- When raising a power to another power, multiply the exponents:
(a^m)^n = a^(mn)
Examples of Squared Numbers
- 3^2 is equal to 3 × 3, which equals 9
- 4^2 is equal to 4 × 4, which equals 16
- 5^2 is equal to 5 × 5, which equals 25
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Description
Learn about exponents and squared numbers, including their definitions, notations, and properties. Understand how to work with exponents and squared numbers in mathematical expressions.
