Express {(4/3)-1 – (1/4)-1}-1 as a rational number.

1.	Express {(4/3)-1 – (1/4)-1}-1 as a rational number.
Answer» {(4/3)^-1 – (1/4)^-1}^-1 We know that, = (4/3)^-1= (3/4)¹… [∵ (a/b)^-n = (b/a)ⁿ] = (1/4)^-1 = (4/1)¹ … [∵ (a/b)^-n = (b/a)ⁿ] Now subtract, = {(3/4) – (4/1)}^-1 = {(3-16)/4}^-1 … [LCM of 4 and 1 is 4] = {-13/4}^-1 = {-4/13}

Answer»

{(4/3)^-1 – (1/4)^-1}^-1

We know that,

= (4/3)^-1= (3/4)¹… [∵ (a/b)^-n = (b/a)ⁿ]

= (1/4)^-1 = (4/1)¹ … [∵ (a/b)^-n = (b/a)ⁿ]

Now subtract,

= {(3/4) – (4/1)}^-1

= {(3-16)/4}^-1 … [LCM of 4 and 1 is 4]

= {-13/4}^-1

= {-4/13}

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