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

Question

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8. 4k^-1+k^-2

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression nine A to the negative fifth plus A to the negative sixth. And we are essentially asked to factor this. So we've got these two terms +98 to the negative fifth and a two. The negative six. And we are going to see what we can factor out. Well, for the whole numbers the coefficients here, there's nine and there's a one. There's nothing we can factor out from those coefficients. Now let's look at the A to the negative fifth and A to the negative six. Well, when we compare A to the negative fifth and A to the negative 6/6 what are we supposed to factor? Well, this is where we look for the common factor with the lowest power. When we have two variables with exponents, we look for the one we the lowest power which is lower negative five or negative six. Well the lower power is negative six. So we're going to factor out a two, the negative sixth. Or in other words we're dividing both of these by A to the negative sixth. Okay, we figured out what's getting factored out. Now let's figure out what's left inside for that first term 98 to the negative fifth. We're dividing that by eight to the negative sixth. We couldn't factor anything out of the nine so we can bring that down now, how about eight to the negative fifth divided by eight. The negative sixth will be recalled previous lessons that when we have variables that are being divided, we are going to take their exponents and subtract them. So we've got negative five minus negative six. Or in other words this is negative five plus six. Negative five plus six is the positive one. So the new exponents is one. We've got a to the first which is the same as a. So we've got nine A. For the first one. Now let's factor out. We've got a to the negative sixth divided by eight to the negative sixth. Again we can subtract those exponents negative six minus negative six. Or in other words negative six plus six, negative six plus six is zero. So exponent is A to the zero while anything raised to the zero power equals one. So this is going to be a nine A plus one that is left after We factored out a to the negative sixth. Alright. Looking for a to the negative six times +98 plus one 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. 4k^-1+k^-2

Key Concepts

Factoring

Least Power of a Variable

Positive Real Numbers

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