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WAEC Mathematics 2013 Paper

Question : 13

Total: 48

Given that

p^{\frac{1}{3}}

\frac{\sqrt[3]{q}}{r}

, make q the subject of the equation

Solution:

Concept:

Rewrite the cube root as a fractional power, then isolate

q

by cubing both sides.

Explanation:

Given:

p^{\frac{1}{3}} = \frac{\sqrt[3]{q}}{r}

Since

\sqrt[3]{q} = q^{\frac{1}{3}}

, we can write

p^{\frac{1}{3}} = \frac{q^{\frac{1}{3}}}{r}

Multiply both sides by

r

r p^{\frac{1}{3}} = q^{\frac{1}{3}}

Cube both sides to remove the fractional power:

\left(r p^{\frac{1}{3}}\right)^3 = \left(q^{\frac{1}{3}}\right)^3

This simplifies to

r^3 \cdot p^{\frac{3}{3}} = q^{\frac{3}{3}}

Since

\frac{3}{3} = 1

, we get

r^3 \cdot p = q

Therefore,

q = pr^3

Answer:

q = pr^3

, which is option C.

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