If x = (1/2)^{-2}÷ (2/3)^{-3}, then what is the reciprocal of x?

Correct Answer is : 273227/323227

Correct Answer is : 273227/323227

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CTET Paper II (Mathematics and Science) 10 Jan 2022 Solved Paper

Question : 35 of 150

Marks: +1, -0

If x =

(\frac{1}{2})^{-2}\div (\frac{2}{3})^{-3}

, then what is the reciprocal of x?

Solution:

Concept:

A negative exponent means take the reciprocal of the base. Dividing by a fraction is same as multiplying by its reciprocal.

Explanation:

First, simplify each term:

(\frac{1}{2})^{-2} = 2^2 = 4

(\frac{2}{3})^{-3} = (\frac{3}{2})^3 = \frac{27}{8}

x = 4 \div \frac{27}{8} = 4 \times \frac{8}{27} = \frac{32}{27}

The reciprocal of

x

\frac{1}{x} = \frac{27}{32}

Answer:

\frac{27}{32}

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