Podcast
Questions and Answers
What is the result of simplifying the expression $x^4 imes x^3$?
What is the result of simplifying the expression $x^4 imes x^3$?
- $x^1$
- $4x^3$
- $x^{12}$
- $x^7$ (correct)
Any base raised to the zero power equals zero.
Any base raised to the zero power equals zero.
False (B)
What happens when you apply the quotient rule to the expression $a^5 / a^2$?
What happens when you apply the quotient rule to the expression $a^5 / a^2$?
$a^3$
$x^{-2}$ can be written as __________.
$x^{-2}$ can be written as __________.
What is the simplified form of $(2^3)^4$?
What is the simplified form of $(2^3)^4$?
The expression $5^0$ is equal to 5.
The expression $5^0$ is equal to 5.
Using the product rule, simplify $y^2 imes y^5$.
Using the product rule, simplify $y^2 imes y^5$.
Match the rules of exponents with their descriptions:
Match the rules of exponents with their descriptions:
What is the result of simplifying $3 imes 4^{-3}$?
What is the result of simplifying $3 imes 4^{-3}$?
The expression $x^{-n} = rac{1}{x^n}$ is always true.
The expression $x^{-n} = rac{1}{x^n}$ is always true.
What is $4^3$?
What is $4^3$?
The expression $2^{-3}$ is equivalent to ___.
The expression $2^{-3}$ is equivalent to ___.
What is the simplified form of $2^3 imes 2^{-5}$?
What is the simplified form of $2^3 imes 2^{-5}$?
Match the expressions with their simplified forms:
Match the expressions with their simplified forms:
Simplify $8^{-1}$. What is the answer?
Simplify $8^{-1}$. What is the answer?
The product $a^m imes a^{n} = a^{___}$.
The product $a^m imes a^{n} = a^{___}$.
What happens to the sign of an exponent when a factor is moved across the fraction bar?
What happens to the sign of an exponent when a factor is moved across the fraction bar?
An exponent applies to all factors in a term, regardless of parentheses.
An exponent applies to all factors in a term, regardless of parentheses.
What is the result of simplifying the expression $x^{-3}$?
What is the result of simplifying the expression $x^{-3}$?
The expression $2^{-2}$ can be rewritten as _____
The expression $2^{-2}$ can be rewritten as _____
Which of the following expressions is equivalent to $\frac{3}{y^{-2}}$?
Which of the following expressions is equivalent to $\frac{3}{y^{-2}}$?
Match the following expressions with their simplifications:
Match the following expressions with their simplifications:
The expression $3^{2} \cdot 3^{-2} = 1$ is true.
The expression $3^{2} \cdot 3^{-2} = 1$ is true.
If $a^{-n} = b$, then $a^n = _____
If $a^{-n} = b$, then $a^n = _____
Flashcards
Product Rule
Product Rule
When multiplying terms with the same base, add the exponents.
Quotient Rule
Quotient Rule
When dividing terms with the same base, subtract the exponents.
Zero Exponent Rule
Zero Exponent Rule
Any non-zero base raised to the power of zero equals one.
Power Rule
Power Rule
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Expanded Power Rule
Expanded Power Rule
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Exponent
Exponent
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Base
Base
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Multiplying Exponents
Multiplying Exponents
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Simplify 3 · 4
Simplify 3 · 4
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Simplify 4^2 · 2^2
Simplify 4^2 · 2^2
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Simplify 2^3 · 2^3
Simplify 2^3 · 2^3
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Simplify 8^3
Simplify 8^3
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Simplify 3^2 · 6^1
Simplify 3^2 · 6^1
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Simplify 10^1.
Simplify 10^1.
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Simplify 7.
Simplify 7.
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Simplify 13^1
Simplify 13^1
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Negative Exponents
Negative Exponents
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Exponent Application
Exponent Application
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Fraction Movement
Fraction Movement
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Example of Negative Exponent
Example of Negative Exponent
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Exponent Scope
Exponent Scope
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Example: a^2 x^3
Example: a^2 x^3
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Example: (ab)^2
Example: (ab)^2
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CAUTION regarding Exponents
CAUTION regarding Exponents
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Study Notes
Exponent Rules & Practice
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Product Rule: To multiply when bases are the same, keep the base and add the exponents. Example: x³ * x⁸ = x¹¹
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Quotient Rule: To divide when bases are the same, keep the base and subtract the exponents. Example: x⁵ / x² = x³
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Zero Exponent Rule: Any base (except zero) raised to the power of zero equals one. Example: y⁰ = 1, 6⁰ = 1
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Power Rule: To raise a power to another power, keep the base and multiply the exponents. Example: (x³)⁴ = x¹²
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Expanded Power Rule: When multiple factors are raised to a power, each factor is raised to that power. Example: (xy)² = x²y²
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Negative Exponents: If a factor is moved from the numerator to the denominator (or vice versa), the sign of the exponent changes. Example: x⁻³ = 1/x³
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Caution: An exponent only applies to the factor immediately next to it unless parentheses enclose other factors. Example: (-3)²=9, but -3²=-9
Exponents Practice Problems and Solutions
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Problem 1: 3 * 4³ = 192
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Problem 2: 4x³ * 2x³ = 8x⁶
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Problem 3: x⁵ * x³ / x⁻¹= x⁷ / x⁻¹ = x⁸
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Problem 4: 2x³ * 2x²= 4x⁵
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Problem 5: 6³ = 216
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Problem 6: 8⁰ = 1
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Problem 7: -(9x)⁰ = -1
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Problem 8: (y⁴)³ = y¹²
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Problem 9: (x²y)⁴ = x⁸y⁴
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Problem 10: 2x⁴ / 4x² = x²
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And many more problems are listed in the document
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