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JAMB 1986 · UME · Q15

Evaluate 913×27−123−16×3−23\dfrac{9^{\frac13} \times 27^{-\frac12}}{3^{-\frac16} \times 3^{-\frac23}}.

Worked solution (try it first)
  1. Write everything as a power of 3: 913=3239^{\frac13} = 3^{\frac23} and 27−12=3−3227^{-\frac12} = 3^{-\frac32}, multiplying the indices.
  2. Top: add the powers, 23−32=4−96\frac23 - \frac32 = \frac{4 - 9}{6}
    =−56= -\frac56, so the top is 3−563^{-\frac56}.
  3. Bottom: −16−23=−56-\frac16 - \frac23 = -\frac56, so the bottom is also 3−563^{-\frac56}.
  4. Top and bottom are equal, so the value is 30=13^0 = 1, option B.

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