Question

if a is positive rational number and n is a positive integer greater than 1,prove that a^n is a rational number.​answer fast

Answer 1

Given :  a is positive rational number and n is a positive integer greater than 1

To prove :$a^n$ is a rational number

Explanation:

we know that the product of the two rational numbers is always a reational number

therefore

if a is the rational number

then

a² = a×a is a  rational number

a³ = a²×a is a  rational number

.

.

.

$a^n = a^n^-^1 \times a$ is a rational number

hence proved

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Answer 2

Answer:

Concept:

p/q of two integers with q 0 can be used to represent a number as a rational number in mathematics. The set of rational numbers also contains all of the integers, which can each be expressed as a quotient with the integer as the numerator and 1 as the denominator.

Step-by-step explanation:

We know that product of two rational numbers is always a rational number.

Hence if a is a rational number then

$a^{2}$ = a x  a is a rational number,

$a^{3}$= 4:2  x a is a rational number.

∴ $a^{n}$=  $a^{n-1}$ x a is a rational number.

Hence proved.

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