Worksheet · solutions includedPercent Change & Exponent Rules — Practice Worksheet
Try each problem first, then click Show solution. To print an answer key, open all solutions before File ▸ Print.
Section A — the questions you missed
Original — Math M1 Q17 (you answered A; correct C)
The population of City A increased by 7% from 2015 to 2016. If the 2016 population is k times the 2015 population, what is k?
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+7% → multiply by 1 + 7/100 = 1.07.
So k = 1.07.
Answer: C) 1.07
Original — Math M1 Q16 (you answered D; correct B)
Which expression is equivalent to 7√(x9y9), where x and y are positive?
- A.x7y7
- B.x(9/7)y(9/7)
- C.x63y63
- D.(xy)7
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A 7th root is the (1/7) power: (x9y9)(1/7).
Multiply exponents: x(9·1/7)y(9·1/7) = x(9/7)y(9/7).
Answer: B) x(9/7)y(9/7)
Section B — new practice (same skills)
Practice 1
A price falls 15%. If the new price is k times the old, what is k?
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−15% → ×(1 − 0.15) = 0.85. k = 0.85.
Answer: 0.85
Practice 2
A value increases 20%, then increases another 10%. Overall multiplier?
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1.20 × 1.10 = 1.32 (a 32% total increase).
Answer: 1.32
Practice 3
Simplify 3√(x6) for x > 0.
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(x6)(1/3) = x(6/3) = x2.
Answer: x2
Practice 4
Write √(x5) as a single power of x.
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√ is the (1/2) power: (x5)(1/2) = x(5/2).
Answer: x(5/2)
Practice 5
Simplify x3 · x4 / x2.
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Add then subtract exponents: 3 + 4 − 2 = 5 → x5.
Answer: x5