Respuesta :
Answer:
Radicals can be expressed as rational exponents and viceversa, that is,
[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]
That allows you to simplify expressions. Let's say, for example, you have:
[tex]\sqrt[6]{4^3}[/tex]
Replacing 4 with 2^2 we get:
[tex]\sqrt[6]{(2^2)^3}[/tex]
[tex]\sqrt[6]{2^{2 \cdot 3}}[/tex]
Rewriting the radical as fractional exponent:
[tex]2^{\frac{2 \cdot 3}{6}} = 2[/tex]
We have that the Radicals can be represented as rational exponents
in order to simplify expressions with radicals
To answer this Question we proceed to first define Radicals or Radical expression and Rational exponents
Radicals
These can simply be defined as an number that us been preceded by a Root symbol or sign ([tex]\sqrt{x}[/tex])
Rational exponents
While Radicals are as stated above Rational exponents are a distinct way of representing radicals by using power fractions ([tex]x^{1/2}[/tex])
Having made the above statements i will now give an illustration of how power rational exponents be applied to simplify expressions with radicals or rational exponents
Let have and expression
[tex]\sqrt{9}*9^2[/tex]
[tex]9^{\frac{1}{2}}*9^2[/tex]
[tex]9^{2\frac{1}{2}}[/tex]
[tex]9^{\frac{3}{2}}[/tex]
We have also apply it inversely to obtain a radical expression
[tex]^2\sqrt{9^3}[/tex]
In conclusion
The Radicals can be represented as rational exponents in order to simplify expressions with radicals
For more information on this please visit
https://brainly.com/question/1369233
