If a^1/n=r then which of the following statements are true

check all that apply

a. r^n=a

b. n^1/r=a

c.^n√a=r

d. a^r=n

a. This is correct. When you transfer n to the other side, that would be the reciprocal power of a.

b. This is incorrect, because this contradicts with choice a.

c. This is correct. When a number is raised to a "1/n" fraction, that is equivalent to the nth root of the number.

d. This is incorrect, because it is not equivalent to the given equation.

Thus, the answers are A and C.

Answer

a. r^n=a

c.^n√a=r

Explanation

solution 1

a⁽¹/ⁿ⁾ = r

Powering both sides of the equation by n;

a⁽¹/ⁿ ₓ ⁿ⁾ = rⁿ

a¹ = rⁿ

solution 2

Also,

a⁽¹/ⁿ⁾ = r

a⁽¹/ⁿ⁾ = ⁿ√a (nth root of a)

ⁿ√a = r