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CTET Paper II (Mathematics and Science) 17 Jan 2022 Solved Paper

Question : 35 of 150

Marks: +1, -0

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

is equal to

Validate

Solution:

Concept:

Simplify the expression using laws of exponents: negative exponents mean reciprocals, and division by a negative exponent is multiplication by its positive power.

Explanation:

First, rewrite the expression step by step.

\left(\frac{3}{4}\right)^{-3} = \left(\frac{4}{3}\right)^3 = \frac{64}{27}

\left(\frac{3}{8}\right)^2 = \frac{9}{64}

3^{-2} = \frac{1}{9}

, so

\div 3^{-2}

means

\times 9

Denominator:

\left(\frac{2}{3}\right)^2 = \frac{4}{9}

and

\left(\frac{4}{3}\right)^{-3} = \left(\frac{3}{4}\right)^3 = \frac{27}{64}

Now combine the numerator:

\frac{64}{27} \times \frac{9}{64} \times 9 = \frac{64}{27} \times \frac{81}{64} = \frac{81}{27} = 3

Denominator:

\frac{4}{9} \times \frac{27}{64} = \frac{108}{576} = \frac{3}{16}

So the expression becomes

3 \div \frac{3}{16} = 3 \times \frac{16}{3} = 16

Answer:

16 (Option C)

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