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WAEC Further Mathematics 2025 Paper

Question : 3

Total: 40

simplfy

\sqrt{(\frac{1}{64}}

^{\frac{-2}{3}}

Solution:

Concept:

When a fraction has a negative exponent, take its reciprocal first; the square root means raising to the power

\frac{1}{2}

Explanation:

The expression is

\left(\sqrt{\frac{1}{64}}\right)^{-\frac{2}{3}}

First compute the square root:

\sqrt{\frac{1}{64}} = \frac{1}{8}

, since

8 \times 8 = 64

\left(\sqrt{\frac{1}{64}}\right)^{-\frac{2}{3}} = \left(\frac{1}{8}\right)^{-\frac{2}{3}}

A negative exponent flips the base:

\left(\frac{1}{8}\right)^{-\frac{2}{3}} = 8^{\frac{2}{3}}

Now

8 = 2^3

, so

8^{\frac{2}{3}} = (2^3)^{\frac{2}{3}} = 2^{3 \times \frac{2}{3}} = 2^2 = 4

Answer:

4

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