Question Details

If x y = ( - 1 3 ) - 3 ÷ ( 2 3 ) - 4 ,  then the value of  ( x y + y x ) - 1 × ( y x ) - 1  is :

Options

A

16548

B

1553

C

1459

D

265/9

Show Answer

Correct Answer :

Option D

265/9

265/9

Solution :

The correct answer is 265/9.

Step 1: Simplify the value of xy

Given the expression for xy:

xy=(-13)-3÷(23)-4

Using the law of exponents (ab)-n=(ba)n, we simplify each part separately:

(-13)-3=(-3)3=-27

(23)-4=(32)4=8116

Now, substitute these simplified values back into the division:

xy=-27÷8116=-27×1681

xy=-163

Step 2: Evaluate the required expression

We square the ratio xy:

(xy)2=(-163)2=2569

Adding 1 to this value gives:

(xy)2+1=2569+1=256+99=2659

Thus, the final simplified value is 265/9.

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