Question

the value of [{x/y}^(√79+√77]^(√79-√77)​

Answer 1

The value of $(\frac{x}{y} )^{\sqrt{79} +\sqrt{77}^{\sqrt{79} - \sqrt{77}}$ is $(\frac{x}{y} )^{2}$.

Step-by-step explanation:

We have,

$(\frac{x}{y} )^{\sqrt{79} +\sqrt{77}^{\sqrt{79} - \sqrt{77}}$  .... (1)

Let a = $\dsqrt{79}$ - $\dsqrt{77}$ and

a = $\dsqrt{79}$ + $\dsqrt{77}$

Equation (1) can be written as,

$(\dfrac{x}{y})^{a} ^{b}$                                                       ...... (2)

= $(\frac{x}{y} )^{ab}$

[ ∵ $(a^{m} )^{n}$ = $a^{mn}$ ]

ab =  $\dsqrt{79}$ - $\dsqrt{77}$ · $\dsqrt{79}$ + $\dsqrt{77}$

= 79 - 77 = 2

Now, (2) becomes

= $(\frac{x}{y} )^{2}$

Hence, the value of $(\frac{x}{y} )^{\sqrt{79} +\sqrt{77}^{\sqrt{79} - \sqrt{77}}$ is $(\frac{x}{y} )^{2}$.