AQA · Mathematics · 8300
GCSE Maths: Indices: fractional
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Indices: fractional (Corbettmaths Video 173), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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What is the value of 4⁻²?
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1/16 (or 0.0625). A negative exponent means reciprocal: 4⁻² = 1/(4²) = 1/16.
What does a⁻ⁿ equal?
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1/aⁿ. A negative exponent means taking the reciprocal of the base raised to the positive exponent.
What is the value of any non-zero number raised to the power of 0?
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1. For example, 25⁰ = 1.
The fractional exponent 36^(1/2) equals ?
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6
What does the fractional exponent a^(1/n) represent?
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The nth root of a. For example, 1000^(1/3) = ³√1000 = 10.
How do you evaluate a^(m/n)?
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Take the nth root of a, then raise to the power m. Equivalently: (ⁿ√a)^m or ⁿ√(a^m).
What is the value of 64^(2/3)?
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16. Find the cube root of 64 (which is 4), then square it: 4² = 16.
What is the value of 49^(-1/2)?
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1/7. First find 49^(1/2) = 7, then apply the negative exponent: 49^(-1/2) = 1/7.
What is the value of 16^0.5?
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4. The exponent 0.5 is the same as 1/2, which means square root.
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