Question

PLEASE HELP Arlene claims that the kth root of x can be expressed as x 1/k. Which equation below justifies Arlene's claim?

(x1k)k=x
(x1k)k=1
(x1k)k=0
(x1k)k=k

Answer 1

The k-th root's inverse function is raising to the k-th power.

So, if we raise the k-th root of some number x to the k-th power, we have applied a function and its inverse to x, and we must get x itself as output:

$f(f^{-1}(x))=f^{-1}(f(x))=x\quad\text{for every invertible function f}$

So, in our case, we have

$(\sqrt[k]{x})^k = \left(x^{\frac{1}{k}}\right)^k=x^{k\cdot \frac{1}{k}}=x^1=x$

Answer 2

The equation that Arlene claim should be $x^{k.\frac{1}{k}} \ = x^1 = x$

Equation:

The k-th root's inverse function should be raising with respect to the k-th power.

Thus, in the case if we raise the k-th root of some number x to the k-th power, so here we used the function and its inverse to x, and we must get x itself in an output:

So,

$(k \sqrt x)^k = (x\frac{1}{k})^k = x^{k.\frac{1}{k}} \ = x^1 = x$

learn more about the expression here: https://brainly.com/question/24686935