Question

If a rational exponent represents the cube root of x^m, where m is a positive integer, how does the rational exponent change as m increases?

The rational exponent ______ as m increases.

a. increases

b. decreases

Answer 1

Option B

Increases

Explanation:

to solve this problem, let us plug in figures to replace the variables in the equation.

Let y be equals to the rational exponent which represents the cube root of x^m,

The equation is given as y =
`\sqrt[3]{x^(m)}`

let x= 3

and m =, 3, 4, and 5

when m = 3, we have
`y =\sqrt[3]{3^(3)} =3`

when m = 4, we have
`y =\sqrt[3]{3^(4)} =4.33`

when m = 5, we have
`y =\sqrt[3]{3^(5)} =6.24`

As we can see, the values of y are increasing. Hence, we can say that the value of the rational exponent increases as y increases