Express (5-1– 7-1)-1 as a rational number.

1.	Express (5-1– 7-1)-1 as a rational number.
Answer» (5^-1– 7^-1)^-1 We know that, = (5)^-1= (1/5)¹… [∵ (a/b)^-n = (b/a)ⁿ] = (7)^-1 = (1/7)¹ … [∵ (a/b)^-n = (b/a)ⁿ] Now subtract, = {(1/5) – (1/7)}^-1 = {(7-5)/35}^-1 … [LCM of 5 and 7 is 35] = {2/35}^-1 = {35/2}

Answer»

(5^-1– 7^-1)^-1

We know that,

= (5)^-1= (1/5)¹… [∵ (a/b)^-n = (b/a)ⁿ]

= (7)^-1 = (1/7)¹ … [∵ (a/b)^-n = (b/a)ⁿ]

Now subtract,

= {(1/5) – (1/7)}^-1

= {(7-5)/35}^-1 … [LCM of 5 and 7 is 35]

= {2/35}^-1

= {35/2}

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