Question on: WAEC Mathematics - 1998

Here's how to simplify the expression: 1. **Rewrite the terms with fractional exponents:** * \\(8^{\\frac{2}{3}} = (2^3)^{\\frac{2}{3}} = 2^{3 \* \\frac{2}{3}} = 2^2 = 4\\) * \\(27^{\\frac{-1}{3}} = (3^3)^{\\frac{-1}{3}} = 3^{3 \* \\frac{-1}{3}} = 3^{-1} = \\frac{1}{3}\\) * \\(64^{\\frac{1}{3}} = (4^3)^{\\frac{1}{3}} = 4^{3 \* \\frac{1}{3}} = 4^1 = 4\\) 2. **Substitute the simplified terms back into the expression:** \\(\\frac{8^{\\frac{2}{3}}\*27^{\\frac{-1}{3}}}{64^{\\frac{1}{3}}} = \\frac{4 \* \\frac{1}{3}}{4}\\) 3. **Simplify the fraction:** \\(\\frac{4 \* \\frac{1}{3}}{4} = \\frac{\\frac{4}{3}}{4} = \\frac{4}{3} \* \\frac{1}{4} = \\frac{1}{3}\\)