When converting rational exponents to radical notation, which of the following are correct? Choose all that apply:
1. Numerator of the rational exponent becomes index of the radical notation
2. Negative exponent of the rational exponent makes the radical notation a negative value
3. Denominator of the radical exponent becomes the power of the radicand in the radical notation
4. Denominator of the rational exponent becomes the index of the radical notation
5. Numerator of the rational exponent becomes power of the radicand in the radical notation

Given:

Converting rational exponents to radical notation.

To find:

The correct statements.

Solution:

According to the property of exponents, conversion of rational exponents to radical notation is

[tex]x^{\frac{a}{b}}=\sqrt[b]{x^a}[/tex]

In [tex]x^\frac{a}{b},[/tex] x is base, a is numerator of the rational exponent and b is denominator of the rational exponent.

In [tex]\sqrt[b]{x^a}[/tex], x is radicand, a is power of radicand and b is index of radical notation.

Denominator of the rational exponent becomes the index of the radical notation.

Numerator of the rational exponent becomes power of the radicand in the radical notation.

Therefore, the correct options are 4 and 5.

Using the conversion of rational exponents to radical notation, it is found that the correct options are:

4. Denominator of the rational exponent becomes the index of the radical notation

5. Numerator of the rational exponent becomes power of the radicand in the radical notation

The conversion of rational exponents to radical notation is modeled by:

[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]

That is:

A negative exponent just is represented by a fraction, as [tex]a^{-\frac{n}{m}} = \frac{1}{a^{\frac{n}{m}}}[/tex], hence the radical is not negative, and item 2 is incorrect.

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