Question 21

If $$x^{y+z} = 1, y^{x+z} = 1024$$ and $$z^{x+y} =729$$(x, y and z are natural numbers), then what is the value of $$(z + 1)^{y+x+1}$$?

Solution

$$x^{y+z}=1$$ from this we can say that , $$x=1\ .$$

And, From $$y^{x+z}=1024\ $$ we can say that :

$$y^{x+z}=2^{10\ }.$$

or, $$y=2\ and\ x+z=10\ .$$

or, $$z=9\ .$$

Now, if we put this value in $$z^{x+y}=729\ equation\ ,$$

it implies that : $$9^{1+2}=9^3=729\ \ .$$

So, Value of x=1, y=2 and z=9 .

So, $$(z+1)^{y+x+1}\ =10^{1+2+1}=10000\ .$$

B is correct choice.

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