## Week 4 in math 10

Fractional Exponents

This week I learnt how to fractional exponents into radicals in order to evaluate it. Here are the steps I used.

First you take your base and place it inside the radicant. Then the bottom half of the fractional exponent (denominator) becomes the index and the top half (numerator) becomes the exponent on the inside of the radicant. You would then find the prime factorization of the base to find the root. You leave the exponent on the inside alone. After that you take the root of the base you now attach the exponent from the inside and place it on the root you found. The last step is to evaluate all that.

And if you were to convert a radical into a single power you would take the radicant which would turn into your base, the index would then become your denominator and the exponent inside would become your numerator.

## Week 3 in math 10

Exponents

This week in math 10 we started a new unit on exponents. And one thing that really stuck out for me is using the laws to simplify equations. It also helps to know what to do when you chose the law.

Laws:

Multiplication law – When you 2 or more variables with the same base and are sitting side by side, but different exponents all you need to do is keep the same base and add all the exponents together. (ex. $5^3$ x $5^5$ = $5^8$) (3+5=8)

Division law – When you 2 or more variables with the same base and have one on top of the other but have different exponents all you need to do is keep the base and subtract the exponents and whichever side has the bigger exponent is where you place what’s left of the exponents. (ex. $2^9$ ÷ $2^3$ = $2^6$) (9-3=6)

Power of a power law – When you have an equation with brackets and have an exponent on the inside and the outside of the brackets all you need to do is times the outside exponent by the inside exponents. (ex. ($5^3$)$^2$ = $5^6$) (3×2=6)

Zero exponent law – When you have a variable the zero as the exponent it always equals 1, because there are no copies of the variable so you times the exponent by the coefficient. (ex. $7^0$ = 1)

After knowing how to use these laws it now becomes easier to simplify equations.

## Week 2 in math 10

Week 2 in math 10

Something that I learned this week is how to convert entire radicals into mixed radicals and vice-versa. In the beginning, I was a bit confused but after doing the homework and asking my classmates for help I began to understand.

This is the process I use to convert the entire radical. First, I would use prime factorization on the radicand, then from there I would look at the index, for example,  in $\sqrt[4]{48}$ the index is 4, meaning that after finding the prime factorization of 48 you would look for the same prime numbers and place them in groups of 4.(Depending on the index given that indicates how many prime numbers are placed in one group.) The prime numbers that are in a group are placed on the outside of the radical which becomes the coefficient, and all the remainders that were not grouped are either multiplied together or left alone. If the remainders are multiple different groups of prime numbers you multiply them, but if there is only one group of the same prime number there’s nothing to multiply it by so you leave it as it is. The remainders stay on the inside of the radical.

Ex.