Perform the indicated operation, and write each answer in lowest ...

Question

Perform the indicated operation, and write each answer in lowest terms. 2x/5 * 10/x^2

Accepted Answer

Hey everyone for the following expression were asked to perform multiplication and simplify the answer. Were given 13 a squared over 23 times over a cubed. Alright, so rewriting what we're given 13 a squared over 23 times 69 over a cubed. Now when we're multiplying fractions together. Okay. It's the same as multiplying fractions with numbers. Just because we have these A's in here, doesn't mean we treat it any differently. So we can multiply straight across the numerator, straight across the denominator. We're gonna have 13 a squared times 69 divided by 23. They cute. All right now, but we notice if we're looking at the coefficients first. Okay, we have 13 times 69 divided by 23. We know that 69 is actually divisible by 23 it's gonna give us three. Okay, so we're looking just at the coefficient coefficient of 13 and we have 69 divided by 23 is gonna give us three. So we have 13 times three. Okay, And if you didn't notice that right off the bat, you could have multiplied 13 times 69 then done the division later. Um the numbers are just gonna get bigger and be a little bit messier to work with. Um but it will work out the same in the end. Okay, Now for dealing with these A's. And what happens when we have exponents with the same base. And we're dividing. Remember the quotient rule for exponents A to the exponent M divided by a to the exponent and is going to give us a to the exponents m minus N. Okay so when we're dividing we can turn this into a single term where we subtract the exponents. So this is gonna give us a. to the exponent 2 -3. Okay. The exponent in the numerator minus the exponent in the denominator And if we simplify this is going to give us 39/8 to the exponent -1. And recall that if we have a negative exponents A. A. To the exponent negative end. Okay we can flip this into the denominator and make the exponent positive. So we have one over a. To the exponent N. Okay now the one over only applies to the base and the exponent. Okay so when we do one over we don't move the 39. So this is going to be 39 divided by a. Okay. All right, so our simplified expression is going to be 39 over a. And that is going to correspond with answer choice. B. Thanks everyone for watching. I hope this video helped see you in the next one.

Perform the indicated operation, and write each answer in lowest terms. 2x/5 * 10/x^2

Key Concepts

Multiplication of Fractions

Simplifying Fractions

Variable Exponents

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