Rational Exponents

Radicals

Radical Expressions

Multiplying Radicals

Radical Equations

Complex Numbers

"The principal goal of education is to create men who are capable of doing new things,
not simply of repeating what other generations have done."
--- Jean Piaget

Study Tips:

Tip 1: Use Study Groups

Tip 2: Use Video Lectures

Tip 3: Explain material
to others




Rational Exponents


The laws for rational exponents work exactly the same as the laws for integer exponents. Here is a review of the laws of exponents



Exponent Laws


Product Law

Power to a Power

Product to a Power

Quotient Law

Quotient to a Power


All rational exponents can be rewritten as radicals. So, your main question is probably, "How do I convert a rational expoent to a radical?" We are so glad you asked.


Let's look at this problem



To convert a rational exponent to a radical the denominator becomes the index(the number in the crevest) and the numerator of the exponent stays with the number or varable and is in the radicand


So =


You notice how there is no number in the crevest. When there is no number in the crevest. It is understood to be a 2.


Lets try coverting more rational exponents to radicals



Example 1



What number becomes the index of the radical?



What number can multiply 4 times in a row to get 81?


= 3





Example 2



What radical will be equal to this rational exponent?


here we find the square root of the numerator and the square root of the denominator.


=


So much fun!



Example 3



What radical will be equal to this rational exponent?



To find the square root of negative 4 we must ask ourselves what two identical numbers multiply together to give us -4. Hmmmm. Lets see if we can find a pair. and

Well, the truth is that there are no real numbers that we can square and get -4. Thus, the answer is "no real solution"



Example 4



The difference between this example and the previous example is the following. In the previous example negative 4 was INSIDE parenthesis. In this example the negative is outside parenthesis, and thus the fractional exaponent is only applied to the 4 not the negative sign.


What radical will be equal to this rational exponent?


= -2



Example 5



What radical will be equal to this rational exponent?



First get the square root of 4 which is 2



Then raise 2 to the 5th power.


= 32


Good job!



Example 6



Here we have a negative exponent. Well using the rules of exponents, a negative exponent causes the fraction to shift. What is in the numerator moves to the denominator and vise versa.


=


We have seen a few half powers by now so we should know that this converts to the square root.


=


Pretty easy huh?



Example 7



Here we have a negative exponent. Well using the rules of exponents, a negative exponent causes the fraction to shift. What is in the numerator moves to the denominator and vise versa.


=


Next, we convert this to a radical.



The cube root of negative 27 is -3


= 9



Example 8



The laws of exponents tells us that we should add the fractions.


=


Rewind to prealgebra. To add fractions of different denominators we need a common denominator

In this case the common denominator is 6.


= = =


What radical will be equal to this rational exponent?


=


The cube root of 8 is 2


= 4


Not bad.



Example 9



What does the laws of exponents tells us to do with the exponents?


Subtract. Bring the smaller number to the greater number and subtract.



We need a common denominator. The common denominator is 20.



Simplify.



=


In math, we do not like to leave radicals in the exponents. So, we will talk about how to do that in the next section.



Example 10



Distribute



Simplify.


= =


So much fun.


Below (is/are) video(s) that will help you understand more.




Thank you for visiting supergenuis99.com

Contact: supergenius99@gmail.com Email Us