Question

Why is the nth root of a number equal to the 1/nth power of that number?​

Answer 1

Answer:

If a is a real number with at least one nth root, then the principal nth root of a , written as n√a , is the number with the same sign as a that, when raised to the nth power, equals a . The index of the radical is n .

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Answer 2

• The nth √root of a

is a number that, when raised to the nth power, givesa

. For example, −3 is the 5th root of −243 because

$\tt (−3)5=−243$. If a is a real number with at least one nth root, then the principal nth root of a is the number with the same sign as a that, when raised to the nth power, equals a.

The principal nth root of a is written as $n√a$, wheren

is a positive integer greater than or equal to 2. In the radical expression,n is called the index of the radical.