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Questions and Answers
What is the Product of Powers Rule?
What is the Product of Powers Rule?
x^(m + n) = x^m * x^n
State the Power of a Power Rule.
State the Power of a Power Rule.
(x^m)^n = x^(m × n)
What is the Quotient of Powers Rule?
What is the Quotient of Powers Rule?
x^m ÷ x^n = x^(m - n)
Explain the Laws of Exponents for Exponents with Different Bases involving division.
Explain the Laws of Exponents for Exponents with Different Bases involving division.
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What is the rule for raising a power to a fractional exponent?
What is the rule for raising a power to a fractional exponent?
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Study Notes
Exponents and Powers
Exponents, also known as powers, refer to repeated multiplication of a number by itself. They can be expressed with notation like x^n, where 'x' is the base and 'n' indicates how many times it has been multiplied by itself. Exponents play a significant role in mathematics, particularly in algebra and calculus, because they allow us to simplify complex expressions and analyze patterns more easily.
The following sections will cover the fundamental laws of exponents, which help us understand and manipulate exponent expressions effectively. These laws ensure consistency when working with exponents and make calculations faster and easier by applying common sense principles.
Laws of Exponents
Product of Powers Rule
If n > m, then x^(m + n) = x^m * x^n = x^m × x^n = x^(m + n).
Power of a Power Rule
(x^m)^n = x^(m × n).
Quotient of Powers Rule
If n > m, then x^m ÷ x^n = x^(m - n).
Laws of Exponents for Exponents with Different Bases
If m and n are integers, and p is a positive real number, then:
- x^m / y^m = (x / y)^m.
- x^m × y^m = (xy)^m.
Laws of Exponents for Exponents with Different Bases
If m and n are integers, and p and q are positive real numbers, then:
- x^m / y^m = (x / y)^m.
- (x^m)^n = x^(m × n).
Laws of Exponents for Exponents with Different Bases
If m and n are integers, and p and q are positive real numbers, then:
- (x^m)^(1/n) = x^(m/n).
- x^m / y^(m - n) = x^m × y^(-n).
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Description
Test your knowledge of the fundamental laws of exponents and powers with this quiz. Explore rules like product of powers, power of a power, quotient of powers, and more. Enhance your understanding of how to simplify and manipulate exponent expressions effectively.
