Respuesta :
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:
- The numerator becomes the power of the radicand, hence item 5 is correct.
- The denominator becomes the index of the radical notation, hence item 4 is correct.
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.
A similar problem is given at https://brainly.com/question/13133871
