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Test: Roots and rational exponents

This test focuses on nth roots and powers with rational exponents. Students apply exponent laws, determine conditions under which expressions are defined and rationalise denominators.

Question qty: 10
Duration in minutes: 16
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Sample questions

  • What restriction applies to an even root over the reals?
  • Calculate ⁿ√a : ⁿ√b, where n = n.
  • Calculate the nth root of the mth root of v.
  • Rationalise the denominator: 1/√n.
  • Calculate a^(m/n).
  • Calculate ⁿ√a · ⁿ√b, where n = n.
  • Which identity relates a rational exponent and a root?
  • Calculate the nth root of v.
  • Simplify a^m · a^n, where m = m, n = n.

Roots and rational exponents

A rational exponent is related to a root by aᵐ⁄ⁿ = ⁿ√(aᵐ). Over the real numbers, an even root requires a non-negative radicand, while an odd root also accepts negative values.

Exponent rules

Add exponents when multiplying powers with the same base, subtract them when dividing, and multiply them when raising a power to a power. A negative exponent denotes a reciprocal. Preserve domain conditions when simplifying: √(a²) = |a|, not always a.

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