Question

How do you express a rational exponent as a radical expression?

a) Take the square root of the exponent
b) Raise the base to the power of the exponent
c) Divide the exponent by the base
d) Take the reciprocal of the exponent

Answer 1

To express a rational exponent as a radical expression, use the property that taking the nth root of a number is equivalent to raising that number to the power of 1/n.

Step-by-step explanation:

To express a rational exponent as a radical expression, we can use the property that taking the nth root of a number is equivalent to raising that number to the power of 1/n.

The general rule is that if we have a rational exponent of the form a/b, where a and b are integers, we can express it as the bth root of the base raised to the ath power. Mathematically, it can be written as:

`x^(a/b) = root(b)(x^a)`

For example, if we have
`x^(2/3)`can express it as the cube root of
`x^2` ince 2/3 is equivalent to 2 * (1/3), which is the power needed to yield a result of
`x^2`we take the cube root.