WAEC 2019 · Paper 2 · Q1

(a)
Simplify: $\dfrac{625^{\left(\frac{3x}{4} - 1\right)} + 125^{(x - 1)}}{5^{(3x - 2)}}$ .

Worked solution (try it first)

Write the numbers as powers of 5: $625^{\frac{3x}{4} - 1} = 5^{4\left(\frac{3x}{4} - 1\right)}$
$= 5^{3x - 4}$ and $125^{x - 1} = 5^{3x - 3}$ .
The top is $5^{3x - 4} + 5^{3x - 3}$ .
Take out the smaller power: $5^{3x - 4}(1 + 5) = 6 \times 5^{3x - 4}$ .
Divide by the bottom, subtracting the indices: $\dfrac{6 \times 5^{3x - 4}}{5^{3x - 2}} = 6 \times 5^{-2}$ .
$5^{-2} = \frac{1}{25}$ , so the answer is $\dfrac{6}{25}$ .