Question

how can an expression written in either radical form or rational exponent form be rewritten into equivalent forms?

Answer 1

An expression in radical form can be converted to rational exponent form by representing the radical as a fraction, for example, the square root of x (
`√(x)`) is x raised to the power of 1/2 (x¹²). We use simple rules for multiplying, dividing, and raising to powers when working with exponents and radicals to rewrite expressions in equivalent forms.

Step-by-step explanation:

An expression written in radical form can be rewritten in an equivalent rational exponent form, and vice versa. For instance, the square root of a number, say x, can be represented as
`√(x)` which is the same as x raised to the power of 1/2, or x¹². The rules for handling these expressions include:

When multiplying two exponents with the same base, we add the exponents.

When dividing exponentials, we subtract the exponents of the exponential terms.

When raising an exponent to another power, we multiply the exponents.

These rules are the basics of dealing with expressions involving exponents and radicals, making it easier to manipulate and simplify equations.

Answer 2

You can convert between radical and rational by remembering a simple example that will help you with any problem. We know that the square root of x has an understood index of 2 and power on the x of 1. When we want to convert to a rational exponent the index becomes the denominator and the power becomes the numerator. So sqrt x = x^(1/2)
Another example: sqrt x^3 = x^(3/2)