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Rational Exponents quiz

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  • How can the square root of a number be expressed using exponents?
    The square root of a number can be written as the number raised to the power of one-half.
  • What is a rational exponent?
    A rational exponent is an exponent that is a fraction, representing both a power and a root.
  • How do you convert the cube root of 13 to an exponent?
    The cube root of 13 is written as 13 to the one-third power, or 13^(1/3).
  • What does the denominator of a fractional exponent represent?
    The denominator represents the index or root of the radical.
  • What does the numerator of a fractional exponent represent?
    The numerator represents the power of the term inside the radical.
  • How would you write the square root of x as an exponent?
    The square root of x is written as x^(1/2).
  • How do you convert y squared under a fifth root to a rational exponent?
    It becomes y^(2/5), with 2 as the numerator and 5 as the denominator.
  • What is the relationship between squaring a number and taking its square root?
    Squaring and taking the square root are inverse operations.
  • How do you convert 5^(1/2) to a radical expression?
    5^(1/2) is equivalent to the square root of 5.
  • What happens when you square 5^(1/2)?
    You get 5, because (5^(1/2))^2 = 5^(1/2*2) = 5^1.
  • How do you convert a radical with an invisible index to a rational exponent?
    The invisible index is 2 for square roots, so the exponent is 1/2.
  • How do you convert 13^(1/3) to a radical?
    13^(1/3) is the cube root of 13.
  • How do you convert a radical expression with a variable to a rational exponent?
    The variable under the root becomes the base, and the exponent is 1 divided by the index.
  • What is the general rule for converting radicals to rational exponents?
    The power inside the radical becomes the numerator, and the index becomes the denominator.
  • Why are rational exponents also called fractional exponents?
    Because they are written as fractions, representing both a power and a root.