Laws of Exponents
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Questions and Answers

What is the result of (3^2 × 3^4)?

  • 3^6
  • 3^8 (correct)
  • 3^(2 + 4)
  • 3^5
  • What is the value of (2 × 3)^2?

  • 2 × 3^2
  • 4 × 9 (correct)
  • 2^2 × 3^2
  • 2^2 × 3
  • What is the result of 2^5 ÷ 2^2?

  • 2^3
  • 2^(2 - 5)
  • 2^7
  • 2^(5 - 2) (correct)
  • What is the value of (3^2)^3?

    <p>3^(2 × 3)</p> Signup and view all the answers

    What is the value of a^0?

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

    Study Notes

    Laws of Exponents

    Product of Powers

    • When multiplying two or more exponential expressions with the same base, add the exponents:
      • a^m × a^n = a^(m + n)
    • Example: 2^3 × 2^4 = 2^(3 + 4) = 2^7

    Power of a Product

    • When raising a product to a power, raise each factor to that power:
      • (ab)^m = a^m × b^m
    • Example: (2 × 3)^2 = 2^2 × 3^2 = 4 × 9 = 36

    Quotient of Powers

    • When dividing two exponential expressions with the same base, subtract the exponents:
      • a^m ÷ a^n = a^(m - n)
    • Example: 2^5 ÷ 2^3 = 2^(5 - 3) = 2^2

    Power of a Power

    • When raising an exponential expression to a power, multiply the exponents:
      • (a^m)^n = a^(m × n)
    • Example: (2^3)^2 = 2^(3 × 2) = 2^6

    Zero Exponent Rule

    • Any nonzero number raised to the power of 0 is equal to 1:
      • a^0 = 1 (where a ≠ 0)
    • Example: 2^0 = 1

    Laws of Exponents

    Product of Powers

    • Multiplying exponential expressions with the same base involves adding the exponents.
    • Formula: a^m × a^n = a^(m + n)
    • Example: 2^3 × 2^4 = 2^(3 + 4) = 2^7

    Power of a Product

    • Raising a product to a power involves raising each factor to that power.
    • Formula: (ab)^m = a^m × b^m
    • Example: (2 × 3)^2 = 2^2 × 3^2 = 4 × 9 = 36

    Quotient of Powers

    • Dividing exponential expressions with the same base involves subtracting the exponents.
    • Formula: a^m ÷ a^n = a^(m - n)
    • Example: 2^5 ÷ 2^3 = 2^(5 - 3) = 2^2

    Power of a Power

    • Raising an exponential expression to a power involves multiplying the exponents.
    • Formula: (a^m)^n = a^(m × n)
    • Example: (2^3)^2 = 2^(3 × 2) = 2^6

    Zero Exponent Rule

    • Any nonzero number raised to the power of 0 is equal to 1.
    • Formula: a^0 = 1 (where a ≠ 0)
    • Example: 2^0 = 1

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    Description

    Learn about the rules of exponents, including product of powers, power of a product, and quotient of powers. Practice examples and exercises to understand the concepts.

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