x/y=(-1/3)^{-3}÷ (2/3)^{-4} then what is the value of (x/y+y/x)^{-1} ?

Correct Answer is : −48265-48/265−26548

Correct Answer is : −48265-48/265−26548

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CTET Paper II (Mathematics and Science) 21 Jan 2024 Solved Paper

Question : 49 of 150

Marks: +1, -0

\frac{x}{y}=(\frac{-1}{3})^{-3}\div (\frac{2}{3})^{-4}

(\frac{x}{y}+\frac{y}{x})^{-1}

Solution:

Concept:

Use laws of exponents:

(\frac{a}{b})^{-n} = (\frac{b}{a})^{n}

and order of operations. Then take the reciprocal of the sum.

Explanation:

First, simplify

\frac{x}{y} = \left(\frac{-1}{3}\right)^{-3} \div \left(\frac{2}{3}\right)^{-4}

\left(\frac{-1}{3}\right)^{-3} = \left(\frac{-3}{1}\right)^{3} = (-3)^3 = -27

\left(\frac{2}{3}\right)^{-4} = \left(\frac{3}{2}\right)^{4} = \frac{81}{16}

Now divide:

-27 \div \frac{81}{16} = -27 \times \frac{16}{81} = -\frac{16}{3}

Thus

\frac{x}{y} = -\frac{16}{3}

, so

\frac{y}{x} = -\frac{3}{16}

Find the sum:

\frac{x}{y} + \frac{y}{x} = -\frac{16}{3} - \frac{3}{16} = -\left(\frac{256}{48} + \frac{9}{48}\right) = -\frac{265}{48}

Now take its reciprocal:

\left(\frac{x}{y}+\frac{y}{x}\right)^{-1} = \left(-\frac{265}{48}\right)^{-1} = -\frac{48}{265}

Answer:

Option A:

-\frac{48}{265}

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