This week in math 10 we learned about integral exponents (negative exponents) and how to get rid of them.
To get rid of negative exponents you need to take the base and flip it.
Example: Whatever your variable or base is, it on it’s own is equal to itself over 1. You just don’t write it as such. So when you flip it, you take whatever is in the numerator, and move it to the denominator, or the other way around. This switch makes the exponent positive.
This same principle of moving a base with an integral exponent to the other position applies to solving other expressions as well. This includes expressions where there are bases/exponents in both the numerator and denominator.
Example: Using the same principle of moving a base with a negative exponent to the other position, we move our negative exponent from the numerator to the denominator, changing the negative to a positive, and then evaluating as you would a normal expression.
This week in math we learned how to convert entire radicals into mixed radicals.
First, find two factors of your radicand, one being a perfect square. Then you will have two radicals, one giving you a whole number, and the other not. This will give you your mixed radical.
Example: In this case you need to find a factor of 75 that is also a perfect square. 25 x 3 is equal to 75, and 25 is also a perfect square. Therefore you square root 25 and move the whole number to the outside of the radical. Therefore 5 x the square root of 3 is equal to the square root of 75.
The same thing can be done with radicals which contain any index. Instead of finding a factor of the radicand that is a perfect square, you find a factor that is either a perfect cube, perfect 4th, etc. depending on the index.
Example: To simplify the cube root of 48, you first need to find a factor of 48 that is a perfect cube. 8 x 6 is equal to 48, and 8 is a perfect cube. You then cube root 8, and again move the number to the outside of the radical. So 2 x the cube root of 6 is equal to the cube root of 48.