Using Properties of Exponents

Using Properties of Exponents

By Rachel Patel and Nora Schulze

​Problem #39

​First you want to distribute the -2 to the exponents within the parentheses by multiplication.

Res​ulting in q^-4 and u^-8.

​Negative exponents create imaginary numbers. In order to stop that you will move the negative exponents into the denominator.

In this case, both move down so a one is left in the numerator.

​The end result should look like this

​Problem #40

​First you want to distribute the -5 to the exponents within the parentheses by multiplication.

Res​ulting in a^30 and b^-40.

​Similar to the last problem, we have a negative exponent. This time, we leave the a^30 in the numerator because it is positive and move b^-40 down to make it positive.

​The end result should look like this

​Problem #41

​Unlike the other problems, the exponents are being multiplied, which means we will add the exponents with like bases. In this case, the x bases add their exponents and same with the y bases. The 2 and 5 multiply regularly. This would result in 10x^14y^-5

​Again, there is a negative exponent in the numerator which we will bring down to the denominator. The 10x^14 will say in the numerator.

​The end result should look like this

​Problem #42

​First, add the like bases together, but keep the numerator and denominator separated. Multiply coeffients regularly

​Next, divide 1584 by 66 regularly; resulting in 24. Then, subtract the bases in the numerator by the bases in the denominator. For example, x^8 - x^10 = x ^-2.

​Finally, move the x^-2 to the denominator to make it a positive 2. Leave the 24y^5.

​The end result looks like this

​Practice Problem #1

​Practice Problem #1 Solution

​To start, we will subtract the exponents in the numerator by the ones in denominator. We will also simplify 5/15 to 1/3 since it is not divisible.

​Next, we will move the -2 to the denominator to make it positive.

​The end result should look like this

​Practice Problem #2

​Practice Problem #2 Solution

​For this problem we need to distribute the -6 to the other exponents by multiplication. It should look like a^18 and q^-24.

​Since the -24 is in the numerator, we need to move it down to the denominator like the problems before.

​The end result should look like this.

​Practice Problem #3

​First we distribute the 4 and -3 to their respective parentheses.

​Practice Problem #3 Solution

​Next, we subtract the exponents in the numerator by the ones in the denominator. Remember, two negatives make a positive. So 8 - (- 3) becomes 8 + 3

​Sine the 15 is negative, we need to move it into the denominator.

​The end result should look like this.

​Practice Problem #4

​Pracitce Problem #4 Solution

​Since we are multiplying the two fractions, we will add the exponents with like bases together. Do not cross the numerator and denominator.

​Now we need to simplify the problem by dividing 6/3 and subtracting the like bases. Remember, 2 negatives make a positive.

​The end result should look like this.