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. 8^2/3

Accepted Answer

Hey everyone in this problem, we are asked to consider the given expression and simplify the expression were given is 16,807 to the exponents to over five. All right, so just rewriting what we're given, 16,807 to the exponent to over five. Now, when we look at this exponent to fifth, we don't really know how to deal with that. Okay, But let's recall our power rule for exponents. If we have a to the exponents M times N. We can break this down and take a to the exponent. M. All to the exponent end. Okay. So it allows us to kind of separate the two parts of that exponent and work with them one at a time. Now we have 2/5. We want to write this as something time something. Well, we can write 2/5 as two times 1/5. Okay. 2/5 is equal to two times 1/5. So now we can break our exponents into two into 1/5. So Rewriting this, we go 16,807 to the exponent. 1/5. Okay. And all of this is going to be squared. Now we could have done this in the other order. We could have had the exponent to inside the bracket and the exponent 1/5 outside the bracket. Okay, we're looking at multiplication. We know that we can change the order when we multiply. However this is a really big number. Okay, so two square it it's only gonna get bigger and then we're gonna take the route to make it smaller. If we do the route first, we're gonna have a smaller number to work with when we go to square it. Okay. So that's why we've chosen that. But either way it's gonna work out to the equivalent answer. Now, we've taken our Exponent of 2/5 which we didn't know how to deal with, and we've broken it into two things we do know how to deal with. Okay, inside the bracket we have this one over a number. We know that that's equivalent to a route. We know how to deal with roots. And then on the outside we have um an exponent of a whole number. Okay? We're just squaring and we know how to do that. We know what that means. So let's go ahead and work inside the brackets first. So we're gonna take the fifth root of 16,807 and that's gonna be seven. Okay? If we take seven to the exponent five, we get 16,807. So the fifth root of 16,807 is seven. And so we have seven squared and we know that seven squared is going to be equal to 49. All right, So our expression simplified is just going to be equal to 49 and that's going to correspond with answer B. That's it for this one. Thanks everyone for watching. See you in the next video

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. 8^2/3

Key Concepts

Exponents and Powers

Negative Exponents

Radical Expressions

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