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JAMB Mathematics 2011 Paper

Question : 5

Total: 46

Simplify

\left( \frac{16}{81} \right)^{\frac{1}{4}} \div \left( \frac{9}{16} \right)^{-\frac{1}{2}}

Solution:

Concept:

Simplify powers and negative exponents using index laws.

Explanation:

Start with the expression.

\left( \frac{16}{81} \right)^{\frac{1}{4}} \div \left( \frac{9}{16} \right)^{-\frac{1}{2}}

Rewrite the negative exponent by taking the reciprocal.

\left( \frac{16}{81} \right)^{\frac{1}{4}} \div \left( \frac{16}{9} \right)^{\frac{1}{2}}

Express both bases as powers of

2

and

3

\left( \frac{2^4}{3^4} \right)^{\frac{1}{4}} \div \left( \frac{4^2}{3^2} \right)^{\frac{1}{2}}

Apply the power to each part.

\frac{2^{4 \times \frac{1}{4}}}{3^{4 \times \frac{1}{4}}} \div \frac{4^{2 \times \frac{1}{2}}}{3^{2 \times \frac{1}{2}}}

This simplifies to:

\frac{2}{3} \div \frac{4}{3}

Change division to multiplication by the reciprocal.

\frac{2}{3} \times \frac{3}{4}

Cancel the

3

and simplify.

\frac{2}{4} = \frac{1}{2}

Answer:

\frac{1}{2}

Option B.

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