The reciprocal of [(3/8)^{-2}× (-4/5)^{-3}]is:

Correct Answer is : −9125-9/125125−9

Correct Answer is : −9125-9/125125−9

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CTET Paper II (Mathematics and Science) Sep 2014 Solved Paper

Question : 43 of 150

Marks: +1, -0

[(\frac{3}{8})^{-2}\times (\frac{-4}{5})^{-3}]

is:

Solution:

Concept:

Reciprocal of a number is 1 divided by that number. To find the reciprocal of an expression, simplify it first and then invert.

Explanation:

Start with

[(\frac{3}{8})^{-2}\times (\frac{-4}{5})^{-3}]

Apply the rule

a^{-n} = \frac{1}{a^n}

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

and

(\frac{-4}{5})^{-3} = (\frac{-5}{4})^{3}

Now multiply:

(\frac{8}{3})^{2} \times (\frac{-5}{4})^{3} = \frac{64}{9} \times \frac{-125}{64} = \frac{-125}{9}

The reciprocal of

\frac{-125}{9}

\frac{9}{-125} = \frac{-9}{125}

Answer:

\frac{-9}{125}

(Option C)

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