Question on: WAEC Mathematics - 1998
Simplify (\frac{8^{\frac{2}{3}}*27^{\frac{-1}{3}}}{64^{\frac{1}{3}}})
A
-3
B
\(\frac{1}{9}\)
C
\(\frac{1}{3}\)
D
\(\frac{27}{8}\)
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Correct Option: C
Here's how to simplify the expression:
-
Rewrite the terms with fractional exponents:
- \(8^{\frac{2}{3}} = (2^3)^{\frac{2}{3}} = 2^{3 * \frac{2}{3}} = 2^2 = 4\)
- \(27^{\frac{-1}{3}} = (3^3)^{\frac{-1}{3}} = 3^{3 * \frac{-1}{3}} = 3^{-1} = \frac{1}{3}\)
- \(64^{\frac{1}{3}} = (4^3)^{\frac{1}{3}} = 4^{3 * \frac{1}{3}} = 4^1 = 4\)
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Substitute the simplified terms back into the expression: \(\frac{8^{\frac{2}{3}}*27^{\frac{-1}{3}}}{64^{\frac{1}{3}}} = \frac{4 * \frac{1}{3}}{4}\)
-
Simplify the fraction: \(\frac{4 * \frac{1}{3}}{4} = \frac{\frac{4}{3}}{4} = \frac{4}{3} * \frac{1}{4} = \frac{1}{3}\)
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