WAEC 2012 Mathematics · Question 6

Solve ( $\frac{27}{125}$ )- $\frac{1}{3}$ x ( $\frac{4}{9}$ ) $\frac{1}{2}$

Options

A. $\frac{10}{9}$
B. $\frac{9}{10}$
C. $\frac{2}{5}$
D. $\frac{12}{125}$

Answer: A. $\frac{10}{9}$

Explanation written with AI and checked against the answer key

The question has lost its formatting, so I'm reading it as: (27/125)^(-1/3) × (4/9)^(1/2). Step 1: Handle the negative index. A negative power means "take the reciprocal": (27/125)^(-1/3) = (125/27)^(1/3) Step 2: Handle the fractional index. The power 1/3 means the cube root: (125/27)^(1/3) = ∛125 / ∛27 = 5/3 Step 3: Evaluate the second part. (4/9)^(1/2) = √4 / √9 = 2/3 Step 4: Multiply. 5/3 × 2/3 = 10/9 Answer: A (10/9) Tip: Handle the negative sign first by flipping the fraction, then read the fractional power as a root (the denominator of the index is the root: 1/3 is a cube root and 1/2 is a square root). Learn the common cubes (27 = 3³, 125 = 5³) because they come up often in WASSCE and JAMB.

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Solve (27125\frac{27}{125}12527​)-13\frac{1}{3}31​ x (49\frac{4}{9}94​)12\frac{1}{2}21​

Options

Answer: A. 109\frac{10}{9}910​

Solve ( $\frac{27}{125}$ )- $\frac{1}{3}$ x ( $\frac{4}{9}$ ) $\frac{1}{2}$

Answer: A. $\frac{10}{9}$