Question

Solve this
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Answer 1

To find the value of x^-2, first, we need to find the value of x. Let's calculate it step by step:

x = (3/2)^2 × (2/3)^-4

x = (9/4) × (1 / (2/3)^4)

x = (9/4) × (1 / (16/81))

x = (9/4) × (81/16)

Now, calculate x:

x = 81/64

Now, to find x^-2, simply take the reciprocal of x and square it:

x^-2 = (1 / (81/64))^2

x^-2 = (64/81)^2

x^-2 = 4096/6561

The value of x^-2 is 4096/6561

Answer 2

Heya There!

Solution:

`(16)/(81)`

Given:

`x = ({ (3)/(2) })^(2) * ({ (2)/(3) })^( - 4)`

To find:

`value \: of \: {x}^( - 2)`

To find the value of x^-2 we need to solve the given value of x:

`x = ( { (3)/(2) })^(2) * ( { (2)/(3) })^( - 4)`

`x=(3)/(2)*(3)/(2)*(-(2)/(3))*(-(2)/(3))*(-(2)/(3))*(-(2)/(3) )`

`x = (9)/(4) * (16)/(81)`

`x = (4)/(9)`

Now, finding the value of x^-2 :-

putting value of x in x^-2,

`{x}^( - 2) = ({ (4)/(9) })^( - 2)`

`x = ( { (2)/(3) })^(2 * - 2)`

`x = ({ (2)/(3) })^( - 4)`

`x = - (2)/(3) * - (2)/(3) * - (2)/(3) * - (2)/(3)`

`x = (16)/(81)`

Hence, the value of x^-2 is 16/81..

Hope this helps you ;) !

Carry on learning :)