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 2 Math and Science 21 Jan 2024 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 to simplify the given expression, then substitute into the required reciprocal sum.

Explanation:

First, simplify

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

Recall

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

. So,

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

and

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

Therefore,

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

Thus,

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

Now compute

S = \frac{x}{y} + \frac{y}{x} = -\frac{16}{3} - \frac{3}{16} = -\frac{256}{48} - \frac{9}{48} = -\frac{265}{48}

Finally,

S^{-1} = \left(-\frac{265}{48}\right)^{-1} = -\frac{48}{265}

Answer:

Option A:

-\frac{48}{265}

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