If a and b are positive integer such that a^b=125, then (a-b)^a+b-4​ is equal to

Dear Student,

Please find below the solution to the asked query :

$$\begin{gathered} \mathrm{We} \mathrm{have}, {\mathrm{a}}^{\mathrm{b}}=125 \\ \Rightarrow {\mathrm{a}}^{\mathrm{b}}=5^3 \\ \mathrm{On} \mathrm{comparing}, \mathrm{a}=5 \mathrm{and} \mathrm{b}=3 \\ \mathrm{Now}, \\ {\left(\mathrm{a}-\mathrm{b}\right)}^{\mathrm{a}+\mathrm{b}-4}={\left(5-3\right)}^{5+3-4} \\ =2^4 \\ =16 \\ \Rightarrow {\left(\mathbf{a}\mathbf{-}\mathbf{b}\right)}^{\mathbf{a}\mathbf{+}\mathbf{b}\mathbf{-}\mathbf{4}}\mathbf{=}\mathbf{16} \end{gathered}$$

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