lesson
A fractional exponent connects roots and powers
1 · Learn
For positive a, a^(1/n) is the positive nth root of a, and a^(m/n) combines that root with power m. Restricting the base to positive values avoids ambiguities that arise with negative bases and some fractional exponents.
Keep the index laws consistent and distinguish the denominator's root from division of the base. a^(1/2) is not a/2.
2 · Worked example
27^(2/3) = 3² = 9, because the cube root of 27 is 3.
3 · Your turn
Evaluate 16^(3/4).
Check your answer
8, because the fourth root of 16 is 2 and 2³ = 8.
4 · Apply your learning
Check a result by relating it back to integer powers and state the domain being used.
Adult guidance and safety
This sequence includes extension mathematics and assumes secure earlier work. Check prerequisite understanding and the learner's readiness before assigning extension tasks. Require derivations, accurate diagrams and varied practice; a correct short example is not full assessment evidence. Exam-board and tier-specific pathways are outside this edition.
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