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

Question

Perform the indicated operation, and write each answer in lowest terms. y^3/8 ÷ y/4

Accepted Answer

Hey everyone in this problem for the following expression were asked to perform division and simplify the answer. And the expression were given is D. To the exponent nine divided by 35 divided by D. To the exponent for over seven. Alright so just writing out what we're giving due to the experiment 9/35. Okay. Divided by D. to the exponent for over seven. Now recall if we have two fractions being divided? So say we have a over B divided by C. Over D. Okay we can invert the denominator and multiply. Okay. So what I mean by that is we can do a over B. Time's D. Oversee. Okay these are equivalent. So dividing by the fraction you can flip it and multiply. So if we apply that to our expression we have D. To the exponent 9/35. And we can multiply this by seven over D. To the exponent four. Okay so we flip and we multiply just like we would with regular fractions. Okay, just because we have a variable in here of D. We don't need to change how we work with these things. Okay. All right now we have two fractions. Multiply together. We can just multiply straight across. This is gonna give us seven D. To the exponent nine divided by 35 d. to the exponent for all right let's give ourselves some more room to work. Now we're dealing with the coefficient in front this 7/35. Okay notice that we can divide both by seven. If we do that we're going to end up with 1/5 for that coefficient. And then when we're dealing with this D. To the exponent nine divided by D. To the exponent four. Okay recall that if we have something with the same base so we have a to the exponent M divided by a. To the exponent N. Care quotient rule for exponents tells us that we can write this as A. To the exponents M minus N. So D. To the exponent nine divided by D. To the exponent four. We can write this as D. To the exponent nine minus four because we've simplified it into one term and simplifying that exponent, we have 1/5 D. To the exponent five. And that's going to be our simplified expression. So if we go back up to our answer choices and we see that our simplified expression is going to be D over five. Or sorry. D. To the exponent five divided by five, which is answer C. 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. y^3/8 ÷ y/4

Key Concepts

Rational Expressions

Dividing Fractions

Simplifying Expressions

Watch next