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Numerade Educator

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Problem 3 Medium Difficulty

Use the Law of Exponents to rewrite and simplify the expression.

(a) $ b^8 (2b)^4 $
(b) $ \dfrac{(6y^3)^4}{2y^5} $

Answer

a) 16$b^{12}$
b) 648$y^{7}$

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Video Transcript

all right, We're going to use laws of exponents to simplify both of these expressions, and they both involve the following law. So if you have a product raised to a power that's equivalent to raising each factor to the power, so let's use that in part a. C. Here we have to be raised to the fourth power. That's equivalent to to to the fourth power times be to the fourth power. So we have the beat of the eighth that's already sitting there, and then we have to to the fourth power times be to the fourth power to to the fourth. Power is 16 and then we can use our exponents law that says you should add the powers eight and four and you get be to the 12th. So altogether we have 16 B to the 12th and then for part B. We're going to use that same rule again that we saw a minute ago and will use it on the six y cubed and will raise six to the fourth power and will raise why cubed to the fourth power six to the fourth power is 1296 for why cube to the fourth power. You're going to use the power rule and multiply those and you get why? To the 12th power. And that's over. Two. Why? To the fifth power. Now we can reduce 12 96 divided by two. And that works out to be 6 48 And then we can use the quotient rule for exponents. Why? To the 12 divided by y to the fifth. We're going to subtract those powers on. We get wide of the seventh power. So altogether we have 648. Why? To the seventh power.