# If a is a positive rational number and n is a positive integer greater than 1, prove that an is a rational number.

a is a positive rational number (Given)

The product of two rational numbers is always a rational number. Hence if a is a rational number then-

a 2 = a × a is also a rational number,
a 3 = a 2 × a is also a rational number,
a 4 = a 3 × a is also a rational number,

a n = a n-1 × a is a rational number.

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