If =2 ⁻¹ 1 8 +2 ⁻¹ 1 5 + ⁻¹ 1 7 and 2 = m + n , where m and n are positive integers such that m < n , then (m^n+n^m )^ m+n is equal to

Step-by-step solution

Given, aligned & =2 ⁻¹ ( 1 8 )+2 ⁻¹ ( 1 5 )+ ⁻¹ ( 1 7 ) & =2 [ ⁻¹ 1 8 + ⁻¹ 1 5 ]+ ⁻¹ 1 7 & =2 ⁻¹ [ 1 / 8+1 / 5 1-1 / 40 ]⁻¹+ ⁻¹ 1 / 7 & =2 ⁻¹ 1 3 + ⁻¹ 1 7 & = ⁻¹ ( 2 / 3 1-1 / 9 )+ ⁻¹ 1 / 7 & = ⁻¹ ( 3 4 )+ ⁻¹ 1 7 & = ⁻¹ ( 3 / 4+1 / 7 1-3 / 28 ) & = ⁻¹(1)= 4 2 & = _ 8 = m + n aligned aligned & ( 8 )= 2 -1= m + n , when m < n & m = 2 and n =-1 & m=2, n=1 & (m^n+n^m )^ m+n = (1^2+2^1 )^3=3^3=27 aligned