A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
(1/2x^2)^3(8x^3)^2
anonymous
 5 years ago
(1/2x^2)^3(8x^3)^2

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay Zechariah, if I've read correctly, you have this: \[\left( \frac{1}{2x^2} \right)^3(8x^3)^2\]You need to use power laws to simplify. If you have\[\left( \frac{a}{b} \right)^n\]this will be equal to\[\frac{a^3}{b^3}\]Also, if you have\[(ab)^n\]this will be equal to\[a^nb^n\]and if you have\[(a^m)^n\]this will be equal to \[a^{mn}\]You can apply these two laws to what you've got. So,\[\left( \frac{1}{2x^2} \right)^3=\frac{1}{(2x^2)^3}=\frac{1}{2^3(x^2)^3}=\frac{1}{8x^6}\]and \[(8x^3)^2=(1)^2(8)^2(x^3)^2=64x^6\]So your expression becomes\[\left( \frac{1}{2x^2} \right)^3(8x^3)^2=\frac{1}{8x^6} \times 64x^6=\frac{64x^6}{8x^6}=\frac{8 \times 8 x^6}{8x^6}=8\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Above I said\[\left( \frac{a}{b} \right)^n=\frac{a^3}{b^3}\]It doesn't; it's a typo. It should read,\[\left( \frac{a}{b} \right)^n=\frac{a^n}{b^n}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0PS: I like your "About Me" statement :) You have the right attitude.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.