Simplify each expression. Write answers without negative exponent...

Question

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. -81^3/4

Accepted Answer

Hey everyone welcome back in this problem. We are asked to consider the given expression. And simplifying the expression were given is negative 64 to the experiment 56. So negative 64 to the exponent 56. Okay, I'm just gonna go ahead. That negative kind of is out in front. Okay. It's not in brackets. It's not the exponent does not apply to it. Okay, so I'm just going to put it out in front and put brackets around everything else just so we don't mix up where that negative is supposed to be. Okay? So if negative 64 to the exponents 5/6. All right now we have this fractional exponents. Okay we want to try to break that up into different components so that we can deal with it more simply. So let's recall our power rule for exponents. If we have a to the exponents M times N. We can write this as a to the exponents. M all to the exponent. Hi now in our case we have 56 and we can think of 56 as being equal to five times 1/6. Okay, so we can break that into two components and exponent of five and an exponent of 1/6. So we can write this as -64. To the exponent 1/6. All to the exponent five. Now the reason I've chosen to put the 16 1st and deal with that exponent first. Um is just because this is a big number 64. Okay, so to do 64 to the exponent five, you're getting into bigger numbers. Whereas if we do this 1/6 1st our number is going to get a little bit smaller first. It'll be easier to work with when we do that. Exponent five. Now we've Changed our exponent 56 which we really didn't know how to deal with. Okay, into two things that we know how to deal with. Okay, we have an exponent of a whole number five, we know how to do that, we know what that means. And we have this exponent of one over a number. Okay. We know that when we have won over a number this is equivalent to a route which we also know how to deal with. Okay, so now we can do this piece by piece. Now like I just said recall that if we have a to the exponent one over end This is equivalent to the end route of a. Okay so when we have negative 64 Um and sorry the negatives out front, when we're looking at 64 to the exponent 16, this is like the six root of 64. Okay, and that's just going to be equal to two. So we have negative and then we have two to the exponent five. So to to the experiment six gives us 64. So the sixth root of 64 is two. Alright now we just have to work this out, we have negative two to the exponent five. We know that two to the exponent five is 32 so we get negative 32. So the simplified version of our expression, it simplifies all the way down to negative 32. And so our answer is going to be c negative 32. Thanks everyone for watching. I hope this video helped see you in the next one.

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. -81^3/4

Key Concepts

Exponents and Radicals

Negative Exponents

Simplifying Expressions

Watch next