Exponent Rules & Practice
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Questions and Answers

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.

    False (B)

    What happens when you apply the quotient rule to the expression $a^5 / a^2$?

    $a^3$

    $x^{-2}$ can be written as __________.

    <p>$1/x^2$</p> Signup and view all the answers

    What is the simplified form of $(2^3)^4$?

    <p>$2^{12}$ (B)</p> Signup and view all the answers

    The expression $5^0$ is equal to 5.

    <p>False (B)</p> Signup and view all the answers

    Using the product rule, simplify $y^2 imes y^5$.

    <p>$y^7$</p> Signup and view all the answers

    Match the rules of exponents with their descriptions:

    <p>Product Rule = Add the exponents when multiplying Quotient Rule = Subtract the exponents when dividing Zero Exponent Rule = Any base to the zero power is one Power Rule = Multiply the exponents when raising to a power</p> Signup and view all the answers

    What is the result of simplifying $3 imes 4^{-3}$?

    <p>0.1875 (D)</p> Signup and view all the answers

    The expression $x^{-n} = rac{1}{x^n}$ is always true.

    <p>True (A)</p> Signup and view all the answers

    What is $4^3$?

    <p>64</p> Signup and view all the answers

    The expression $2^{-3}$ is equivalent to ___.

    <p>1/8</p> Signup and view all the answers

    What is the simplified form of $2^3 imes 2^{-5}$?

    <p>$2^{-2}$ (C)</p> Signup and view all the answers

    Match the expressions with their simplified forms:

    <p>$2^{-1}$ = 1/2 $3^{-2}$ = 1/9 $5^{-3}$ = 1/125 $4^{-4}$ = 1/256</p> Signup and view all the answers

    Simplify $8^{-1}$. What is the answer?

    <p>1/8</p> Signup and view all the answers

    The product $a^m imes a^{n} = a^{___}$.

    <p>m+n</p> Signup and view all the answers

    What happens to the sign of an exponent when a factor is moved across the fraction bar?

    <p>It changes to a positive exponent. (A)</p> Signup and view all the answers

    An exponent applies to all factors in a term, regardless of parentheses.

    <p>False (B)</p> Signup and view all the answers

    What is the result of simplifying the expression $x^{-3}$?

    <p>$\frac{1}{x^3}$</p> Signup and view all the answers

    The expression $2^{-2}$ can be rewritten as _____

    <p>$\frac{1}{4}$</p> Signup and view all the answers

    Which of the following expressions is equivalent to $\frac{3}{y^{-2}}$?

    <p>$3y^2$ (C)</p> Signup and view all the answers

    Match the following expressions with their simplifications:

    <p>$5^{-1}$ = $\frac{1}{5}$ $x^{-4}$ = $\frac{1}{x^4}$ $a^{-3}$ = $\frac{1}{a^3}$ $3^{-2}$ = $\frac{1}{9}$</p> Signup and view all the answers

    The expression $3^{2} \cdot 3^{-2} = 1$ is true.

    <p>True (A)</p> Signup and view all the answers

    If $a^{-n} = b$, then $a^n = _____

    <p>$\frac{1}{b}$</p> Signup and view all the answers

    Flashcards

    Product Rule

    When multiplying terms with the same base, add the exponents.

    Quotient Rule

    When dividing terms with the same base, subtract the exponents.

    Zero Exponent Rule

    Any non-zero base raised to the power of zero equals one.

    Power Rule

    When raising a power to a power, multiply the exponents.

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    Expanded Power Rule

    Raising a power to a power multiplies the exponents.

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    Exponent

    A number representing how many times a base should be multiplied by itself

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    Base

    The number being raised to a power.

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    Multiplying Exponents

    When bases are the same, add their exponents.

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    Simplify 3 · 4

    Calculate the product of 3 and 4. The answer is 12.

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    Simplify 4^2 · 2^2

    Calculate 4 to the power of 2, then 2 to the power of 2, and then multiply the results. The answer is 64.

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    Simplify 2^3 · 2^3

    Calculate 2 to the power of 3 twice and then multiply. The answer is 64.

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    Simplify 8^3

    Calculate 8 multiplied by itself 3 times. The answer is 512.

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    Simplify 3^2 · 6^1

    Calculate the results to the power and multiply. The answer is 54.

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    Simplify 10^1.

    Calculate the product. The answer is 10

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    Simplify 7.

    The answer is 7.

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    Simplify 13^1

    13^1 is computed by multiplying 13 by itself once. The answer is 13.

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    Negative Exponents

    When a factor is moved across a fraction bar, the sign of the exponent changes.

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    Exponent Application

    An exponent applies only to the factor immediately beside it, unless parentheses enclose other factors.

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    Fraction Movement

    Moving a factor from the numerator to the denominator (or vice versa) changes the sign of its exponent.

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    Example of Negative Exponent

    If you have '1/ x^n', moving x^n to the numerator makes it 'x^-n'

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    Exponent Scope

    The exponent only affects the factor immediately to its left unless contained in parentheses.

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    Example: a^2 x^3

    The exponent 2 applies only to a, the exponent 3 applies only to x.

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    Example: (ab)^2

    The exponent 2 applies to both a and b.

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    CAUTION regarding Exponents

    An exponent only applies to the adjacent factor unless the adjacent factor is enclosed in parentheses.

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    Study Notes

    Exponent Rules & Practice

    • Product Rule: To multiply when bases are the same, keep the base and add the exponents. Example: x³ * x⁸ = x¹¹

    • Quotient Rule: To divide when bases are the same, keep the base and subtract the exponents. Example: x⁵ / x² = x³

    • Zero Exponent Rule: Any base (except zero) raised to the power of zero equals one. Example: y⁰ = 1, 6⁰ = 1

    • Power Rule: To raise a power to another power, keep the base and multiply the exponents. Example: (x³)⁴ = x¹²

    • Expanded Power Rule: When multiple factors are raised to a power, each factor is raised to that power. Example: (xy)² = x²y²

    • 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

    • 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

    • Problem 1: 3 * 4³ = 192

    • Problem 2: 4x³ * 2x³ = 8x⁶

    • Problem 3: x⁵ * x³ / x⁻¹= x⁷ / x⁻¹ = x⁸

    • Problem 4: 2x³ * 2x²= 4x⁵

    • Problem 5: 6³ = 216

    • Problem 6: 8⁰ = 1

    • Problem 7: -(9x)⁰ = -1

    • Problem 8: (y⁴)³ = y¹²

    • Problem 9: (x²y)⁴ = x⁸y⁴

    • Problem 10: 2x⁴ / 4x² = x²

    • And many more problems are listed in the document

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    Related Documents

    Exponent Rules & Practice PDF

    Description

    Test your knowledge of exponent rules with this quiz! You'll explore essential concepts such as the Product Rule, Quotient Rule, and the Zero Exponent Rule through practice problems and solutions. Boost your understanding of exponential expressions.

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