Algebra Exponent Laws Flashcards
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Questions and Answers

What does the expression x²⁴ represent?

  • x to the power of 2
  • x to the power of 24 (correct)
  • x squared
  • x to the power of 48
  • What does the expression a⁸b¹² simplify to?

    a to the power of 8 times b to the power of 12

    What is represented by the term 2c⁷?

    2 times c to the power of 7

    What does the expression 15x⁸ represent?

    <p>15 times x to the power of 8</p> Signup and view all the answers

    What is the definition of x⁷y⁷?

    <p>x to the power of 7 times y to the power of 7</p> Signup and view all the answers

    What does the expression 9x² simplify to?

    <p>9 times x squared</p> Signup and view all the answers

    What does a⁴ represent?

    <p>a raised to the power of 4</p> Signup and view all the answers

    What is represented by a²¹b⁶?

    <p>a to the power of 21 times b to the power of 6</p> Signup and view all the answers

    What does 4c⁵ represent?

    <p>4 times c to the power of 5</p> Signup and view all the answers

    What is x¹¹?

    <p>x raised to the power of 11</p> Signup and view all the answers

    What does the expression x²⁰ simplify to?

    <p>x raised to the power of 20</p> Signup and view all the answers

    What does a⁸ represent?

    <p>a raised to the power of 8</p> Signup and view all the answers

    What does a¹⁸b⁶ represent?

    <p>a to the power of 18 times b to the power of 6</p> Signup and view all the answers

    What does the expression 3u²⋅8u⁶ simplify to?

    <p>24u⁸</p> Signup and view all the answers

    What is the result of (−3d)(5d⁵)(−d³)?

    <p>15d⁹</p> Signup and view all the answers

    What does (10x⁸y⁵) / (-2xy²) simplify to?

    <p>-5x⁷y³</p> Signup and view all the answers

    What does (24a²b) / (6ab) simplify to?

    <p>4a</p> Signup and view all the answers

    What is (x²)(x³)?

    <p>x⁵</p> Signup and view all the answers

    What does 5x⁴/x² simplify to?

    <p>5x²</p> Signup and view all the answers

    What is the result of (7x²)(x³)?

    <p>7x⁵</p> Signup and view all the answers

    What does (3x⁴)⁵ equal?

    <p>3⁵x²⁰</p> Signup and view all the answers

    What is (-7x²)(4x⁴)?

    <p>-28x⁶</p> Signup and view all the answers

    What is x⁸ ÷ x⁵?

    <p>x³</p> Signup and view all the answers

    What does (-2x³y²)(5xy⁴) simplify to?

    <p>-10x⁴y⁶</p> Signup and view all the answers

    What does (6h)⁴ represent?

    <p>6⁴h⁴</p> Signup and view all the answers

    What is (-2x³y²)(5xy⁴)?

    <p>-10x⁴y⁶</p> Signup and view all the answers

    What is 3⁸?

    <p>(3⁵)(3³)</p> Signup and view all the answers

    What does (3³)⁵ equal?

    <p>3¹⁵</p> Signup and view all the answers

    What does (4⁷)² simplify to?

    <p>4¹⁴</p> Signup and view all the answers

    What is 4⁴?

    <p>4⁶ / 4²</p> Signup and view all the answers

    What does 5¹⁰ represent?

    <p>(5²)⁵</p> Signup and view all the answers

    Study Notes

    Exponential Expressions

    • x²⁴ represents a variable x raised to the power of 24.
    • a⁸b¹² defines two variables, a raised to the power of 8 and b raised to the power of 12.
    • 2c⁷ indicates a coefficient of 2 multiplied by the variable c raised to the power of 7.
    • 15x⁸ shows a coefficient of 15 multiplied by the variable x raised to the power of 8.
    • x⁷y⁷ indicates the product of two variables, x and y, each raised to the power of 7.
    • 9x² signifies a coefficient of 9 multiplied by x raised to the power of 2.
    • a⁴ is a single variable a raised to the power of 4.
    • a²¹b⁶ denotes a raised to the power of 21 multiplied by b raised to the power of 6.
    • 4c⁵ consists of a coefficient of 4 and c raised to the power of 5.
    • x¹¹ indicates x raised to the power of 11 and operates independently.
    • x²⁰ represents x raised to the power of 20, a higher exponent than earlier examples.
    • a⁸ is simply a raised to the power of 8, without other variables.
    • a¹⁸b⁶ shows a raised to the power of 18 multiplied by b raised to the power of 6.

    Simplifying Products and Quotients

    • For the product (3u²)(8u⁶), the simplified result is 24u⁸; combine coefficients and add exponents.
    • The multiplication of (−3d)(5d⁵)(−d³) results in 15d⁹; negative coefficients multiplied yield a positive result.
    • Dividing (10x⁸y⁵) by (−2xy²) simplifies to -5x⁷y³; adjust the signs and reduce the variables.
    • The expression (24a²b) divided by (6ab) simplifies to 4a; reduce coefficients and variables.

    Laws of Exponents

    • The multiplication of powers law (x²)(x³) results in x⁵; add the exponents.
    • Simplifying 5x⁴/x² yields 5x²; subtract the exponents for the same base.
    • The product (7x²)(x³) simplifies to 7x⁵; again, add exponents.
    • Raising a power to a power (3x⁴)⁵ results in 3⁵x²⁰; multiply the exponent.

    Negative Coefficients

    • The expression (-7x²)(4x⁴) simplifies to -28x⁶; multiply coefficients and add exponents.
    • The division x⁸ ÷ x⁵ results in x³; apply the same rules of exponent subtraction.
    • The product (-2x³y²)(5xy⁴) simplifies to -10x⁴y⁶; multiply coefficients and add the exponents of like variables.

    Further Simplification

    • (6h)⁴ simplifies to 6⁴h⁴; distribute the exponent.
    • 3⁸ breaks down into (3⁵)(3³) by adding exponents.
    • (3³)⁵ results in 3¹⁵; another demonstration of power to a power.
    • The expression (4⁷)² simplifies to 4¹⁴; distribute the exponent.
    • 4⁴ can be expressed as 4⁶ / 4², showing the quotient of powers.
    • 5¹⁰ can also be represented as (5²)⁵, reinforcing the power of a power concept.

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