Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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I am requesting step by step instructions on how to solve this. Especially as we work with the whole numbers and try to reduce/simplify. Thanks
Transcribed Image Text:나
b
-3
214
aaa
3k
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Follow-up Question
Can you explain these steps further. how did it get from 4³ to 2⁶ then to 2². How did you end up with 324? Thanks
![Step 1: Determine the simplified value
Given:
\[
\left( \frac{4}{b} \right)^{-3} \left( \frac{2a^2}{3b} \right)^4
\]
Step 2: Calculate the simplified values
Now:
\[
\left( \frac{4}{b} \right)^{-3} \left( \frac{2a^2}{3b} \right)^4
\]
Rewriting using properties of exponents:
\[
= \left( \frac{b}{4} \right)^3 \left( \frac{2a^2}{3b} \right)^4
\]
\[
= \frac{b^3}{4^3} \times \frac{2^4 \, a^8}{3^4 \, b^4}
\]
\[
= \frac{b^3}{64} \times \frac{16 \, a^8}{81 \, b^4}
\]
\[
= \frac{a^8}{324b}
\]
Solution
Hence:
\[
\left( \frac{4}{b} \right)^{-3} \left( \frac{2a^2}{3b} \right)^4 = \frac{a^8}{324b}
\]](https://content.bartleby.com/qna-images/question/a8cc5b47-1a8c-416c-961a-08ac39ec1d30/59a81fd2-186c-4651-a217-5edfb4e06da9/e3rslbe_processed.jpeg)
Transcribed Image Text:Step 1: Determine the simplified value
Given:
\[
\left( \frac{4}{b} \right)^{-3} \left( \frac{2a^2}{3b} \right)^4
\]
Step 2: Calculate the simplified values
Now:
\[
\left( \frac{4}{b} \right)^{-3} \left( \frac{2a^2}{3b} \right)^4
\]
Rewriting using properties of exponents:
\[
= \left( \frac{b}{4} \right)^3 \left( \frac{2a^2}{3b} \right)^4
\]
\[
= \frac{b^3}{4^3} \times \frac{2^4 \, a^8}{3^4 \, b^4}
\]
\[
= \frac{b^3}{64} \times \frac{16 \, a^8}{81 \, b^4}
\]
\[
= \frac{a^8}{324b}
\]
Solution
Hence:
\[
\left( \frac{4}{b} \right)^{-3} \left( \frac{2a^2}{3b} \right)^4 = \frac{a^8}{324b}
\]
Solution
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