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Questions and Answers
What is the result of raising a^m to the power of n?
What is the result of raising a^m to the power of n?
What is the value of a^(-n) according to the Index Laws?
What is the value of a^(-n) according to the Index Laws?
What is the result of simplifying the expression 2^3 × 2^5?
What is the result of simplifying the expression 2^3 × 2^5?
What is the result of raising a to the power of 3/2?
What is the result of raising a to the power of 3/2?
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What is the result of simplifying the expression (3^2)^3?
What is the result of simplifying the expression (3^2)^3?
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What is the result of simplifying the expression 3^2 × 3^4 ÷ 3^2?
What is the result of simplifying the expression 3^2 × 3^4 ÷ 3^2?
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Study Notes
Exponent Rules
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Product Rule: When multiplying two or more exponential expressions with the same base, add the exponents.
- Example:
a^m × a^n = a^(m+n)
- Example:
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Quotient Rule: When dividing two exponential expressions with the same base, subtract the exponents.
- Example:
a^m ÷ a^n = a^(m-n)
- Example:
-
Power Rule: When raising an exponential expression to a power, multiply the exponents.
- Example:
(a^m)^n = a^(mn)
- Example:
Simplifying Expressions
- Simplify expressions by combining like terms and applying the exponent rules.
- Example:
2^3 × 2^5 = 2^(3+5) = 2^8 - Example:
3^2 × 3^4 ÷ 3^2 = 3^(2+4-2) = 3^4
Index Laws
-
Zero Index: Any number raised to the power of 0 is 1.
- Example:
a^0 = 1
- Example:
-
Negative Index: A negative index is equivalent to a reciprocal with a positive index.
- Example:
a^(-n) = 1/a^n
- Example:
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Fractional Index: A fractional index is equivalent to a root of the base.
- Example:
a^(1/n) = nth root of a
- Example:
Squaring And Cubing
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Squaring: When raising a number to the power of 2, multiply it by itself.
- Example:
a^2 = a × a
- Example:
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Cubing: When raising a number to the power of 3, multiply it by itself twice.
- Example:
a^3 = a × a × a
- Example:
-
Simplifying Squares and Cubes: Use the exponent rules to simplify expressions involving squares and cubes.
- Example:
2^3 × 2^2 = 2^(3+2) = 2^5 - Example:
(3^2)^3 = 3^(2×3) = 3^6
- Example:
Exponent Rules
- Exponent rules are used to simplify exponential expressions
- Product Rule: Add exponents when multiplying exponential expressions with the same base
- Quotient Rule: Subtract exponents when dividing exponential expressions with the same base
- Power Rule: Multiply exponents when raising an exponential expression to a power
Simplifying Expressions
- Combine like terms and apply exponent rules to simplify expressions
- Simplify expressions by adding or subtracting exponents when the bases are the same
- Example: Combine
2^3and2^5by adding exponents:2^(3+5) = 2^8
Index Laws
- Zero Index Law: Any number raised to the power of 0 is 1
- Negative Index Law: A negative index is equivalent to a reciprocal with a positive index
- Fractional Index Law: A fractional index is equivalent to a root of the base
Squares and Cubes
- Squaring: Raising a number to the power of 2 is equivalent to multiplying it by itself
- Cubing: Raising a number to the power of 3 is equivalent to multiplying it by itself twice
- Simplify square and cube expressions using exponent rules
- Example:
(3^2)^3can be simplified using the power rule:3^(2×3) = 3^6
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Description
Learn and practice the product, quotient, and power rules of exponents, and simplify expressions by combining like terms.
