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WAEC Mathematics 2012 Paper

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Question : 26

Total: 49

Solve (

\;\frac{27}{125}

)^{- $\;\frac{1}{3}$} x (

\;\frac{4}{9}

)^{$\;\frac{1}{2}$}

$\;\frac{10}{9}$
$\;\frac{9}{10}$
$\;\frac{2}{5}$
$\;\frac{12}{125}$

Solution:

Concept:

Use the laws of exponents:

a^{-n} = \frac{1}{a^n}

and

(a^m)^n = a^{mn}

.

Explanation:

Write each base as a power.

\frac{27}{125} = \frac{3^3}{5^3} = \left(\frac{3}{5}\right)^3

.

So,

\left(\frac{27}{125}\right)^{-\frac{1}{3}} = \left[\left(\frac{3}{5}\right)^3\right]^{-\frac{1}{3}} = \left(\frac{3}{5}\right)^{-1} = \frac{5}{3}

.

Also,

\left(\frac{4}{9}\right)^{\frac{1}{2}} = \sqrt{\frac{4}{9}} = \frac{2}{3}

.

Now multiply the two results.

\frac{5}{3} \times \frac{2}{3} = \frac{10}{9}

.

Answer:

\frac{10}{9}

, which is option A.

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