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Simplification & Approximation · Question 57 of 71

Question 57

HardOriginal question

Evaluate (243)0.8×(32)0.6(81)0.25\dfrac{(243)^{0.8} \times (32)^{0.6}}{(81)^{0.25}}.

Options for question 57

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. 243=35243 = 3^5, so 2430.8=35×0.8=34=81243^{0.8} = 3^{5 \times 0.8} = 3^4 = 81.

  2. 32=2532 = 2^5, so 320.6=25×0.6=23=832^{0.6} = 2^{5 \times 0.6} = 2^3 = 8.

  3. 81=3481 = 3^4, so 810.25=31=381^{0.25} = 3^1 = 3.

  4. Value =81×83=216= \frac{81 \times 8}{3} = 216.

Worth noting

Decimal powers become easy once each base is a clean power: 0.8 of five 3s is four 3s. Taking 810.2581^{0.25} as a square root (9) gives 72.

Concept
Decimal indices by rewriting bases as powers
Typical time
90 s
Your time
—
The rule this testsPowers, roots and surds
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Ten questions from Simplification & Approximation, at your own pace.

Practise this chapter →

Ten questions from Simplification & Approximation, at your own pace.