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Evaluate each problem using your table of powers. 9) 2435 11) (25) + 10) (-27) 2 12) 144².

Evaluate each problem using your table of powers. 9) 2435 11) (25) + 10) (-27) 2 12) 144².

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Were asked to evaluate each problem with our table of powers. Can someone help?
**Evaluate Each Problem Using Your Table of Powers** 9) \( 243^{\frac{5}{3}} \) 10) \( (-27)^{-\frac{2}{3}} \) 11) \( \left(\frac{25}{9}\right)^{-\frac{3}{2}} \) 12) \( (-144)^{\frac{1}{2}} \)
Transcribed Image Text:**Evaluate Each Problem Using Your Table of Powers** 9) \( 243^{\frac{5}{3}} \) 10) \( (-27)^{-\frac{2}{3}} \) 11) \( \left(\frac{25}{9}\right)^{-\frac{3}{2}} \) 12) \( (-144)^{\frac{1}{2}} \)
Title: Understanding Powers in Mathematics --- **Introduction to Powers** This table is an educational tool designed to help students understand and identify patterns in powers of numbers. The table shows various numbers raised to different powers, from \(x^1\) to \(x^{10}\). --- **Table of Powers** | \(x\) | \(x^1\) | \(x^2\) | \(x^3\) | \(x^4\) | \(x^5\) | \(x^6\) | \(x^7\) | \(x^8\) | \(x^9\) | \(x^{10}\) | |---------|--------|--------|--------|----------|--------|--------|--------|--------|--------|----------| | **2** | 2 | 4 | 8 | 16 | 32 | 64 | 128 | 256 | 512 | 1024 | | **3** | 3 | 9 | 27 | 81 | 243 | 729 | 2187 | 6561 | 19683 | 59049 | | **4** | 4 | 16 | 64 | 256 | 1024 | 4096 | 16384 | 65536 | 262144 | 1048576 | | **5** | 5 | 25 | 125 | 625 | 3125 | 15625 | 78125 | 390625 | 1953125| 9765625 | | **6** | 6 | 36 | 216 | 1296 | 7776 | 46656 | 279936 | 1679616| 10077696| 60466176 | | **7** | 7 | 49 | 343 | 2401 | 16807 | 117649 | 823543 | 5764801| 40353607| 282475249| | **8** | 8 | 64 | 512 | 4096 | 32768 |
Transcribed Image Text:Title: Understanding Powers in Mathematics --- **Introduction to Powers** This table is an educational tool designed to help students understand and identify patterns in powers of numbers. The table shows various numbers raised to different powers, from \(x^1\) to \(x^{10}\). --- **Table of Powers** | \(x\) | \(x^1\) | \(x^2\) | \(x^3\) | \(x^4\) | \(x^5\) | \(x^6\) | \(x^7\) | \(x^8\) | \(x^9\) | \(x^{10}\) | |---------|--------|--------|--------|----------|--------|--------|--------|--------|--------|----------| | **2** | 2 | 4 | 8 | 16 | 32 | 64 | 128 | 256 | 512 | 1024 | | **3** | 3 | 9 | 27 | 81 | 243 | 729 | 2187 | 6561 | 19683 | 59049 | | **4** | 4 | 16 | 64 | 256 | 1024 | 4096 | 16384 | 65536 | 262144 | 1048576 | | **5** | 5 | 25 | 125 | 625 | 3125 | 15625 | 78125 | 390625 | 1953125| 9765625 | | **6** | 6 | 36 | 216 | 1296 | 7776 | 46656 | 279936 | 1679616| 10077696| 60466176 | | **7** | 7 | 49 | 343 | 2401 | 16807 | 117649 | 823543 | 5764801| 40353607| 282475249| | **8** | 8 | 64 | 512 | 4096 | 32768 |
Expert Solution
Step 19

NOTE: Refresh your page if you can't see any equations.

.

243^{\frac{3}{5}}

from the table, we can write,  3^5=243

=\left(3^5\right)^{\frac{3}{5}}

use the exponent rule  \left(a^b\right)^c=a^{bc}

=3^{5\cdot \frac{3}{5}}

=3^3

{\color{Red} =27}

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