31 exam-style questions on Rational exponents — topic 1.10 of Number and Algebra in the IB Mathematics: Applications and Interpretation syllabus — with answers and explanations. Samples below; the full set is free with an account.
Determine the exact value of 27^(2/3).
Answer: 9
27^(2/3) = (27^(1/3))² = 3² = 9.
Determine the value of 16^(−1/2).
Answer: 1/4
16^(−1/2) = 1/√16 = 1/4. The negative exponent gives the reciprocal, and the 1/2 gives the square root.
Express √(x⁵) using a rational exponent.
Answer: x^(5/2)
√(x⁵) = (x⁵)^(1/2) = x^(5/2). The root of 2 becomes the denominator of the fractional exponent.
Simplify x^(1/2) · x^(1/3), giving the answer as a single power of x.
Answer: x^(5/6)
Multiplying powers adds exponents: 1/2 + 1/3 = 3/6 + 2/6 = 5/6, so the result is x^(5/6).
Determine the value of 8^(4/3).
Answer: 16
8^(4/3) = (8^(1/3))⁴ = 2⁴ = 16.
Simplify (x^(2/3))³ using the laws of exponents.
Answer: x²
Raising a power to a power multiplies exponents: (2/3)×3 = 2, so the result is x².
That was 6 of 31 Rational exponents questions.
Practise all 31 freeDetermineAO2 · 2–6 marks
Obtain the only possible answer — by calculation, from the graph or by reasoning — and show how.
CalculateAO2 · 2–6 marks
Show the formula, the substitution and the answer with units and sensible significant figures.
SolveAO2 · 2–6 marks
Find the answer with a valid method and show the working; check it against the original question.
31 Rational exponents questions — free with an account. Spaced repetition, streaks and full exam simulations included.
Practise them freeThis platform is independently developed and is not endorsed by, affiliated with, or sponsored by the International Baccalaureate Organization. “International Baccalaureate” and “IB” are registered trademarks of the IBO.