AQA · Mathematics · 8300
GCSE Maths: Indices: negative
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Indices: negative (Corbettmaths Video 175), 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. A negative exponent means the reciprocal: 4⁻² = 1/(4²) = 1/16.
What does a⁻ⁿ equal in terms of positive exponents?
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1/(aⁿ). A negative exponent indicates the reciprocal of the base raised to the positive exponent.
Is 9⁻² equal to −81?
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No. 9⁻² = 1/(9²) = 1/81, not −81. The negative sign applies to the exponent, not the result.
What is the value of any non-zero number raised to the power 0?
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1. For example, 25⁰ = 1.
What does a^(1/n) represent?
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The nth root of a. For example, 27^(1/3) = ∛27 = 3.
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√(aᵐ).
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 (25/16)^(1/2)?
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5/4. Take the square root of numerator and denominator separately: √25/√16 = 5/4.
What is 7 × 7⁰ × 7⁻¹ simplified?
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1. Using exponent laws: 7¹ × 7⁰ × 7⁻¹ = 7^(1+0−1) = 7⁰ = 1.
How do you write 8 in the form 4ⁿ?
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4^(3/2). Since 8 = 2³ and 4 = 2², we have 8 = (2²)^(3/2) = 4^(3/2).
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