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Intro to the Power Rules quiz

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  • What does the power rule state when you have an exponential expression raised to another exponent?
    The power rule states that you multiply the exponents together when an exponential expression is raised to another exponent.
  • How do you simplify (4^3)^2 using the power rule?
    You multiply the exponents: 3 × 2 = 6, so (4^3)^2 = 4^6.
  • What is the simplified form of (-2^3)^5 using the power rule?
    You multiply the exponents: 3 × 5 = 15, so (-2^3)^5 = -2^15.
  • How do you evaluate y^8 raised to the 4th power?
    Multiply the exponents: 8 × 4 = 32, so (y^8)^4 = y^32.
  • What does the power of a product rule allow you to do?
    It allows you to distribute the exponent to each factor in a product inside parentheses.
  • How do you simplify (3 × 4)^2 using the power of a product rule?
    Distribute the exponent: (3 × 4)^2 = 3^2 × 4^2.
  • What is the simplified form of (5 × 3^2)^2?
    Distribute the exponent: 5^2 × (3^2)^2, then use the power rule to get 5^2 × 3^4.
  • How do you simplify (x × y)^5?
    Distribute the exponent: (x × y)^5 = x^5 × y^5.
  • When can you use the power of a product rule?
    You can use it when two or more quantities are multiplied together and the entire product is raised to an exponent.
  • What is the result of (a^m)^n according to the power rule?
    The result is a^(m×n), where you multiply the exponents.
  • How do you simplify (3^2)^4?
    Multiply the exponents: 2 × 4 = 8, so (3^2)^4 = 3^8.
  • What is the first step in simplifying (a × b)^n?
    Distribute the exponent to each factor: (a × b)^n = a^n × b^n.
  • If you have (x^3 × y^2)^4, how do you simplify it?
    Distribute the exponent: (x^3)^4 × (y^2)^4, then use the power rule to get x^12 × y^8.
  • Why is multiplying exponents in the power rule valid?
    Because raising a power to another power means repeated multiplication, which is represented by multiplying the exponents.
  • What is the simplified form of (2 × 5)^3?
    Distribute the exponent: (2 × 5)^3 = 2^3 × 5^3.