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

(a) $ 8^\frac{4}{3} $(b) $ x (3x^2)^3 $

a) 16b) 27$x^{7}$

01:55

Jeffrey P.

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 4

Exponential Functions

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

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Okay, so we want to use exponents rules to simplify these expressions. And so, first of all, if you think about the number eight, think of it as a power of two. So eight is the same as two cubed. So we have two cubed to the 4/3 power. Now, remember, your exponents rule the power rule that says if you have a power to a power, you're going to multiply them. So we're going to multiply three times 4/3 and three times 4/3 is for So now all we have is to to the fourth and that 16 for part B. We're going to raise three x squared to the third power by raising each of those factors to the third power. So we have our X, and then we have three to the third power, and then we have X squared to the third power. And just like we saw in part A, we're going to use the power rule and multiply the powers two and three. So now we have X times three cubed, which is 27 times X to the sixth power. Now, remember that that X in the front is really X to the first power and you can add the exponents on X and you will get X to the seventh. So we have 27 times X to the seventh power.

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