Non-integer exponents (HL only)
Practice Flashcards
What does a negative exponent mean? (x⁻ⁿ)
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All Flashcards in Topic 1.10
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1.10.18 cards
What does a negative exponent mean? (x⁻ⁿ)
A reciprocal: x⁻ⁿ = 1/xⁿ. It does NOT make the value negative.
What is x⁰ (for x ≠ 0)?
1 — anything (non-zero) to the power 0 is 1.
What does x^(1/n) mean?
The n-th root of x: x^(1/n) = ⁿ√x. So x^(1/2) = √x, x^(1/3) = ³√x.
What does x^(m/n) mean?
ⁿ√(xᵐ) = (ⁿ√x)ᵐ — the bottom n is the root, the top m is the power.
Evaluate 27^(2/3).
Cube root of 27 is 3, then square: 3² = 9.
Write √x as a power of x.
x^(1/2). (And ³√x = x^(1/3), 1/√x = x^(−1/2).)
Evaluate 16^(−3/4).
Reciprocal of 16^(3/4): 4th root of 16 is 2, cube it (8), reciprocal = 1/8.
Simplify √x ÷ x² as a single power.
x^(1/2) / x² = x^(1/2 − 2) = x^(−3/2).
Topic 1.10 study notes
Full notes & explanations for Non-integer exponents (HL only)
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