This document discusses powers and radicals. It defines a radical as an expression denoted as , where n is the index and a is the radicand. There are different cases for the number of roots of a radical depending on if the radicand is positive or negative and if the exponent is even or odd. Radicals can be expressed as powers by making the denominator of a fractional exponent equal to the index of the radical. Equivalent radicals are obtained by multiplying or dividing the index and exponent by the same natural number. Simplifying radicals involves dividing out common factors between the index and exponent. Adding and multiplying radicals requires them to have the same index and radicand, while dividing involves reducing to a common index first.

1. BILINGUAL SECTION – MARÍA ESTHER DE LA ROSA
POWERS AND RADICALS
1. POWERS
This is explained in the theory of the past year
2. RADICALS
A radical is an expression denoted as , in which n and a
If the index is “2” it is a square root, if the index is “3” then it¨s a cube root, etc.
3. NUMBER OF ROOTS OF A RADICAL
We have three different cases:
a) Positive radicand and even exponent: Two different solutions
b) Negative radicand and even exponent: It has no solution.
c) Positive radicand and odd exponent: There is only one positive solution.
d) Negative radicand and odd exponent: There is only one negative solution
4. RELATIONSHIP BETWEEN RADICALS AND POWERS
A radical can be expressed in the form of a power:

2. The denominator of a fractional exponent is equal to the index of the radical.
Example:
5. EQUIVALENT RADICALS
If you multiply or divide the index and the exponent of a radical by the same natural number, obtained is another
equivalent radical.
Example:
6. SIMPLIFYING RADICALS
If there is a natural number that divides the index and the exponent (or the exponents) of a radicand, you get a
simplified radical.
7. EXTRACTION OF FACTORS
1. Write the prime factorization of the radicand
2. Re-write each factor so that the powers are all less than or equal to the index.
3. Removing the factors that have a power equal to the index
Example:
8. INTRODUCTION OF FACTORS
To do this operation you must write the factor as a power wich exponent using the index as the exponent.
9. ADDING RADICALS
Two radicals can only be added (or subtracted) when they are radicals with the same index and the same radicand,
that is to say, similar radicals.

3. Example:
10. MULTIPLIYING AND DIVIDING RADICALS
1. First, reduce to a common index:
2. Divide the new index by the other index, then multiply this number by the exponent of the radicand.
Example 1:
Example 2:
11. POWER OF RADICALS
Example:
12. ROOT OF RADICALS
Examples: