Factor out the least power of the variable or variable express...

Question

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8. 4t^-2+8t^-4

Accepted Answer

Welcome back. I am so glad you're here we are. Given this expression 11 D. To the negative third plus 33 D. To the negative ninth. And we are asked to essentially to factor this. So we've got these two terms 11 D. To the negative 3rd and 33 D. To the negative ninth. And we are going to compare the comparable parts. So we've got these coefficients these whole numbers here, we've got 11 And 33. Did they have any common factors? What is the greatest common factor between 11 and 33? Well that is 11. We can divide both of them by 11 so we can factor out. And 11. Now, how about these D. Terms? We've got D. To the negative three and we've got D to the negative ninth. Do they share any common factors? Well, here, when we have variables race two exponents. This is where we're looking for the common factor with the lowest power. So between D to the negative one or negative third and D. To the negative ninth which is the lower power. Well the lower power is negative nine, negative nine is lower than negative three. So we're going to factor out D. To the negative ninth or will divide both of these by D. To the negative ninth. Alright, so we figured out what we're factoring out. Now let's figure out what's left behind once we factored. So let's do the division that we've set up, starting with the first term 11 D. To the negative third divided by 11 D. To the negative 9. 11 divided by 11 is one. How about D. To the negative third divided by D. To the negative nine. Well we recall from previous lessons that when we have variables with exponents and they're being divided we're going to subtract those exponents. We're going to take a negative three minus a negative nine. Or in other words this is negative three plus nine. Well what's negative three plus nine? That is a positive six. So this will be D. To the sixth power. So we've got one times D. To the sixth. Well one times D. To the sixth is D. To the sixth. So I am just going to put D. To the sixth. Alright we've got the first term done. Now let's work on 33 D. To the negative nine divided by 11 D. To the negative nine. 33 divided by 11 equals three. So we've got plus three and now we've got D. To the negative ninth divided by D. To the negative ninth. Again we are going to subtract those exponents so nine minus negative nine. Or in other words excuse me negative nine minus negative nine which is negative nine plus nine and negative nine plus nine is zero. So we've got D raised to the zero. Well anything raised to the zero power equals one. So this is three times one which is three so we can just leave it as three. Alright we've got this factored we are looking for 11 D. To the negative ninth time's D. To the sixth plus three that matches with answer choice. A well done. We'll catch you on the next one.

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8. 4t^-2+8t^-4

Key Concepts

Negative Exponents

Factoring Out the Least Power

Properties of Exponents

Watch next

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8. 4t-2+8t-4

Key Concepts

Negative Exponents

Factoring Out the Least Power

Properties of Exponents

Watch next

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8. 4t^-2+8t^-4