CLASS 9 MATHS · NUMBER SYSTEMS

Fractional and negative exponents

a^(p/q) = (q-th root of a)^p and a^(−n) = 1/aⁿ. Take the root first to keep numbers small.

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Worked examples

Example 1 · level 1

Find the value of 9^(1/2).

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√9 = 3, because 3² = 9.
Answer: 3.

Answer: 3

Example 2 · level 2

Find the value of 81^(3/2).

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√81 = 9, because 9² = 81.
9³ = 729.
Answer: 729.

Answer: 729

Example 3 · level 3

Find the value of 81^(−5/4). (answer as a fraction)

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4th root of 81 = 3, because 3⁴ = 81.
3⁵ = 243.
Negative exponent → reciprocal: 1/243.

Answer: 1/243