# 7. Which of the following imply that the real number x must be rational? I. x, x7are both rational II. x, x are both rational II. x5, x are both rational O I, Il only O I, IlIl only O II, Il only O Il only O None of these combinations Tagged in

7. Which of the following imply that the real number x must be rational? I. x, x7are both rational II. x, x are both rational II. x5, x are both rational
O I, Il only
O I, IlIl only
O II, Il only
O Il only
O None of these combinations Tagged in
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Mitchel Aguirre
Given
The real number x be the rational number .
Let $x=p/q$ and n be the any exponent of x .
${x}^{n}=\left(p/q{\right)}^{n}$
$=\left(p/q\right)\left(p/q\right)\left(p/q\right)\left(p/q\right)...\left(p/q\right)$
${x}^{n}=\left({p}^{n}/{q}^{n}\right)$
Here multiplication of rational number is rational number .
By using above expression
${x}^{5},{x}^{6},{x}^{7},{x}^{8}$ are rational numbers .
There is no option with all conditions.
Therefore , The none of these combination is correct option.