Simplify each exponential expression in Exercises 23–64. x^30/x^−...

Question

Simplify each exponential expression in Exercises 23–64. x^30/x^−10

Accepted Answer

Hi there. This problem says consider to give an exponential expression Aid to the 28th divided by eight to the negative seventh and simplify this expression. So let's take a look at this age the 28th over A To the -7. So I will write this as a fraction. So to simplify this one thing we don't want is negative exponents. We notice that we have a negative exponent a. Into the -7. So we're gonna try and get rid of that to get a simplification. So one of our rules that we should know from our lesson is how to change a negative exponent to a fraction. So right now we have eight to negative seven in the bottom of our affection. That's kind of like saying we have 1/8 to the -7. The age of 28 is still there but I'm going to ignore that just for now and just focus on the age of seven and we have a negative exponents. We can change that to a positive exponent by flipping which part of the fraction the exponent is on. So what I mean by that is if we have an eight to negative seven on the bottom, This turns into a to the positive seven on the top over a one. So we're flipping our fraction over and changing the exponents sign from negative to positive. This is just a to the 7th. Now let's go ahead and bring back our AIDS for 28. So we have 8-28. Aid to the Native seven. I used the same idea. We're flipping our rates and eight of seven up. That's something goes 8-28 times A. To the 7/1 which is just a two the seven. Now we have a case we're multiplying two numbers with exponents in them. So we have eight of the 28 and eight and 7. When you multiply exponents the rule is that we actually add them together. So I should say A. To the end times A. To the M. That is A. To the N. Plus M. Let's go ahead and do that with our actual problem. So if it's A. To the N. Plus M. We have a 2 28 Plus seven. This turns out to be a to the 35th being our answer is a. To the 35th. Or answer a. Alright. I hope to help you solve the problem. Thank you for watching. Goodbye.

Watch next