Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 5.1, Problem 36WE

To determine

To find: To check the given statement is true or not.

Expert Solution & Answer

Answer to Problem 36WE

The given statement is True for all the Law of Exponents.

Explanation of Solution

Given information:

The law of exponents:

am⋅an=am+n(am)n=amnaman=am−n(ab)m=am⋅bm

Replace ⋅ by + and ÷ by −

The first law,

am⋅an=am+n

Left-hand side = a⋅a⋅a⋅⋅⋅a (m..times) ⋅a⋅a⋅⋅⋅a(n..times)

Left-hand side = a+a+a+.....+a(m..times) +a+a+.....+a(n..times)

Left-hand side = ma+na

Left-hand side = (m+n)a

Right-hand side = a⋅a⋅a⋅⋅⋅a((m+n)..times)

Right-hand side = a+a+.....+a((m+n)..times)

Right-hand side = (m+n)a

Therefore, Left-hand side = Right-hand side

The given statement is True for the 1^s^t law.

The 2ⁿ^d law,

(am)n=amn

Left-hand side = [a⋅a⋅a⋅⋅⋅a(m..times)]⋅[a⋅a⋅a⋅⋅⋅a(m..times)]⋅⋅⋅[a⋅a⋅a⋅⋅⋅a(m..times)](n..times)

Left-hand side = [a+a+.....+a(m..times)]+[a+a+.....+a(m..times)]+....+[a+a+.....+a(m..times)](n..times)

Left-hand side = ma+ma+.....+ma(n..times)

Left-hand side = mna

Right-hand side = a⋅a⋅a⋅⋅⋅a(mn..times)

Right-hand side = a+a+.....+a(mn..times)

Right-hand side = mna

Therefore, Left-hand side = Right-hand side

The given statement is True for the 2ⁿ^d law.

The 3^r^d law,

aman=am−n

Left-hand side = [a⋅a⋅a⋅⋅⋅a(m..times)]÷[a⋅a⋅a⋅⋅⋅a(n..times)]

Left-hand side = [a+a+.....+a(m..times)]−[a+a+.....+a(n..times)]

Left-hand side = ma−na

Left-hand side = (m−n)a

Right-hand side = a⋅a⋅a⋅⋅⋅a((m−n)..times)

Right-hand side = a+a+.....+a((m−n)..times)

Right-hand side = (m−n)a

Therefore, Left-hand side = Right-hand side

The given statement is True for the 3^r^d law.

The 4^t^h law,

(ab)m=am⋅bm

Left-hand side = ab⋅ab⋅ab⋅⋅⋅ab(m..times)

Left-hand side = [(a+b)⋅(a+b)⋅(a+b)⋅⋅⋅(a+b)(m..times)]

Left-hand side = (a+b)+(a+b)+.....+(a+b)(m..times)

Left-hand side = (a+b)m

Right-hand side = [a⋅a⋅a⋅⋅⋅a(m..times)].[b⋅b⋅b⋅⋅⋅b(m..times)]

Right-hand side = [a+a+.....+a(m..times)]+[b+b+.....+b(m..times)]

Right-hand side = am+bm

Right-hand side = (a+b)m

Therefore, Left-hand side = Right-hand side

The given statement is True for 4th law.

Therefore,

The given statement is True for all the Law of Exponents.

Chapter 5.1, Problem 35WE

Chapter 5.1, Problem 1MRE

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 5.1 - Prob. 1OE Ch. 5.1 - Prob. 2OE Ch. 5.1 - Prob. 3OE Ch. 5.1 - Prob. 4OE Ch. 5.1 - Prob. 5OE Ch. 5.1 - Prob. 6OE Ch. 5.1 - Prob. 7OE Ch. 5.1 - Prob. 8OE Ch. 5.1 - Prob. 9OE Ch. 5.1 - Prob. 10OE

Ch. 5.1 - Prob. 11OE Ch. 5.1 - Prob. 12OE Ch. 5.1 - Prob. 1WE Ch. 5.1 - Prob. 2WE Ch. 5.1 - Prob. 3WE Ch. 5.1 - Prob. 4WE Ch. 5.1 - Prob. 5WE Ch. 5.1 - Prob. 6WE Ch. 5.1 - Prob. 7WE Ch. 5.1 - Prob. 8WE Ch. 5.1 - Prob. 9WE Ch. 5.1 - Prob. 10WE Ch. 5.1 - Prob. 11WE Ch. 5.1 - Prob. 12WE Ch. 5.1 - Prob. 13WE Ch. 5.1 - Prob. 14WE Ch. 5.1 - Prob. 15WE Ch. 5.1 - Prob. 16WE Ch. 5.1 - Prob. 17WE Ch. 5.1 - Prob. 18WE Ch. 5.1 - Prob. 19WE Ch. 5.1 - Prob. 20WE Ch. 5.1 - Prob. 21WE Ch. 5.1 - Prob. 22WE Ch. 5.1 - Prob. 23WE Ch. 5.1 - Prob. 24WE Ch. 5.1 - Prob. 25WE Ch. 5.1 - Prob. 26WE Ch. 5.1 - Prob. 27WE Ch. 5.1 - Prob. 28WE Ch. 5.1 - Prob. 29WE Ch. 5.1 - Prob. 30WE Ch. 5.1 - Prob. 31WE Ch. 5.1 - Prob. 32WE Ch. 5.1 - Prob. 33WE Ch. 5.1 - Prob. 34WE Ch. 5.1 - Prob. 35WE Ch. 5.1 - Prob. 36WE Ch. 5.1 - Prob. 1MRE Ch. 5.1 - Prob. 2MRE Ch. 5.1 - Prob. 3MRE Ch. 5.1 - Prob. 4MRE Ch. 5.1 - Prob. 5MRE Ch. 5.1 - Prob. 6MRE Ch. 5.1 - Prob. 7MRE Ch. 5.1 - Prob. 8MRE Ch. 5.1 - Prob. 9MRE Ch. 5.1 - Prob. 10MRE Ch. 5.1 - Prob. 11MRE Ch. 5.1 - Prob. 12MRE Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.2 - Prob. 1OE Ch. 5.2 - Prob. 2OE Ch. 5.2 - Prob. 3OE Ch. 5.2 - Prob. 4OE Ch. 5.2 - Prob. 5OE Ch. 5.2 - Prob. 6OE Ch. 5.2 - Prob. 7OE Ch. 5.2 - Prob. 8OE Ch. 5.2 - Prob. 9OE Ch. 5.2 - Prob. 10OE Ch. 5.2 - Prob. 11OE Ch. 5.2 - Prob. 12OE Ch. 5.2 - Prob. 13OE Ch. 5.2 - Prob. 14OE Ch. 5.2 - Prob. 15OE Ch. 5.2 - Prob. 16OE Ch. 5.2 - Prob. 1WE Ch. 5.2 - Prob. 2WE Ch. 5.2 - Prob. 3WE Ch. 5.2 - Prob. 4WE Ch. 5.2 - Prob. 5WE Ch. 5.2 - Prob. 6WE Ch. 5.2 - Prob. 7WE Ch. 5.2 - Prob. 8WE Ch. 5.2 - Prob. 9WE Ch. 5.2 - Prob. 10WE Ch. 5.2 - Prob. 11WE Ch. 5.2 - Prob. 12WE Ch. 5.2 - Prob. 13WE Ch. 5.2 - Prob. 14WE Ch. 5.2 - Prob. 15WE Ch. 5.2 - Prob. 16WE Ch. 5.2 - Prob. 17WE Ch. 5.2 - Prob. 18WE Ch. 5.2 - Prob. 19WE Ch. 5.2 - Prob. 20WE Ch. 5.2 - Prob. 21WE Ch. 5.2 - Prob. 22WE Ch. 5.2 - Prob. 23WE Ch. 5.2 - Prob. 24WE Ch. 5.2 - Prob. 25WE Ch. 5.2 - Prob. 26WE Ch. 5.2 - Prob. 27WE Ch. 5.2 - Prob. 28WE Ch. 5.2 - Prob. 29WE Ch. 5.2 - Prob. 30WE Ch. 5.2 - Prob. 31WE Ch. 5.2 - Prob. 32WE Ch. 5.2 - Prob. 33WE Ch. 5.2 - Prob. 34WE Ch. 5.2 - Prob. 35WE Ch. 5.2 - Prob. 36WE Ch. 5.2 - Prob. 37WE Ch. 5.2 - Prob. 38WE Ch. 5.2 - Prob. 39WE Ch. 5.2 - Prob. 40WE Ch. 5.2 - Prob. 41WE Ch. 5.2 - Prob. 42WE Ch. 5.2 - Prob. 43WE Ch. 5.2 - Prob. 44WE Ch. 5.2 - Prob. 45WE Ch. 5.2 - Prob. 46WE Ch. 5.2 - Prob. 47WE Ch. 5.2 - Prob. 48WE Ch. 5.2 - Prob. 49WE Ch. 5.2 - Prob. 50WE Ch. 5.2 - Prob. 51WE Ch. 5.2 - Prob. 52WE Ch. 5.2 - Prob. 53WE Ch. 5.2 - Prob. 54WE Ch. 5.2 - Prob. 55WE Ch. 5.2 - Prob. 56WE Ch. 5.2 - Prob. 57WE Ch. 5.2 - Prob. 58WE Ch. 5.3 - Prob. 1OE Ch. 5.3 - Prob. 2OE Ch. 5.3 - Prob. 3OE Ch. 5.3 - Prob. 4OE Ch. 5.3 - Prob. 5OE Ch. 5.3 - Prob. 6OE Ch. 5.3 - Prob. 7OE Ch. 5.3 - Prob. 8OE Ch. 5.3 - Prob. 9OE Ch. 5.3 - Prob. 10OE Ch. 5.3 - Prob. 11OE Ch. 5.3 - Prob. 12OE Ch. 5.3 - Prob. 1WE Ch. 5.3 - Prob. 2WE Ch. 5.3 - Prob. 3WE Ch. 5.3 - Prob. 4WE Ch. 5.3 - Prob. 5WE Ch. 5.3 - Prob. 6WE Ch. 5.3 - Prob. 7WE Ch. 5.3 - Prob. 8WE Ch. 5.3 - Prob. 9WE Ch. 5.3 - Prob. 10WE Ch. 5.3 - Prob. 11WE Ch. 5.3 - Prob. 12WE Ch. 5.3 - Prob. 13WE Ch. 5.3 - Prob. 14WE Ch. 5.3 - Prob. 15WE Ch. 5.3 - Prob. 16WE Ch. 5.3 - Prob. 17WE Ch. 5.3 - Prob. 18WE Ch. 5.3 - Prob. 19WE Ch. 5.3 - Prob. 20WE Ch. 5.3 - Prob. 21WE Ch. 5.3 - Prob. 22WE Ch. 5.3 - Prob. 23WE Ch. 5.3 - Prob. 24WE Ch. 5.3 - Prob. 25WE Ch. 5.3 - Prob. 26WE Ch. 5.3 - Prob. 27WE Ch. 5.3 - Prob. 28WE Ch. 5.3 - Prob. 29WE Ch. 5.3 - Prob. 30WE Ch. 5.3 - Prob. 31WE Ch. 5.3 - Prob. 1P Ch. 5.3 - Prob. 2P Ch. 5.3 - Prob. 3P Ch. 5.3 - Prob. 4P Ch. 5.3 - Prob. 5P Ch. 5.3 - Prob. 6P Ch. 5.3 - Prob. 7P Ch. 5.3 - Prob. 8P Ch. 5.3 - Prob. 9P Ch. 5.3 - Prob. 10P Ch. 5.3 - Prob. 11P Ch. 5.3 - Prob. 12P Ch. 5.3 - Prob. 13P Ch. 5.3 - Prob. 14P Ch. 5.3 - Prob. 15P Ch. 5.3 - Prob. 1MRE Ch. 5.3 - Prob. 2MRE Ch. 5.3 - Prob. 3MRE Ch. 5.3 - Prob. 4MRE Ch. 5.3 - Prob. 5MRE Ch. 5.3 - Prob. 6MRE Ch. 5.3 - Prob. 7MRE Ch. 5.3 - Prob. 8MRE Ch. 5.3 - Prob. 9MRE Ch. 5.3 - Prob. 10MRE Ch. 5.3 - Prob. 11MRE Ch. 5.3 - Prob. 12MRE Ch. 5.3 - Prob. 1ST Ch. 5.3 - Prob. 2ST Ch. 5.3 - Prob. 3ST Ch. 5.3 - Prob. 4ST Ch. 5.3 - Prob. 5ST Ch. 5.3 - Prob. 6ST Ch. 5.3 - Prob. 7ST Ch. 5.3 - Prob. 8ST Ch. 5.3 - Prob. 9ST Ch. 5.3 - Prob. 10ST Ch. 5.4 - Prob. 1OE Ch. 5.4 - Prob. 2OE Ch. 5.4 - Prob. 3OE Ch. 5.4 - Prob. 4OE Ch. 5.4 - Prob. 5OE Ch. 5.4 - Prob. 6OE Ch. 5.4 - Prob. 7OE Ch. 5.4 - Prob. 8OE Ch. 5.4 - Prob. 9OE Ch. 5.4 - Prob. 10OE Ch. 5.4 - Prob. 11OE Ch. 5.4 - Prob. 12OE Ch. 5.4 - Prob. 13OE Ch. 5.4 - Prob. 14OE Ch. 5.4 - Prob. 15OE Ch. 5.4 - Prob. 1WE Ch. 5.4 - Prob. 2WE Ch. 5.4 - Prob. 3WE Ch. 5.4 - Prob. 4WE Ch. 5.4 - Prob. 5WE Ch. 5.4 - Prob. 6WE Ch. 5.4 - Prob. 7WE Ch. 5.4 - Prob. 8WE Ch. 5.4 - Prob. 9WE Ch. 5.4 - Prob. 10WE Ch. 5.4 - Prob. 11WE Ch. 5.4 - Prob. 12WE Ch. 5.4 - Prob. 13WE Ch. 5.4 - Prob. 14WE Ch. 5.4 - Prob. 15WE Ch. 5.4 - Prob. 16WE Ch. 5.4 - Prob. 17WE Ch. 5.4 - Prob. 18WE Ch. 5.4 - Prob. 19WE Ch. 5.4 - Prob. 20WE Ch. 5.4 - Prob. 21WE Ch. 5.4 - Prob. 22WE Ch. 5.4 - Prob. 23WE Ch. 5.4 - Prob. 24WE Ch. 5.4 - Prob. 25WE Ch. 5.4 - Prob. 26WE Ch. 5.4 - Prob. 27WE Ch. 5.4 - Prob. 28WE Ch. 5.4 - Prob. 29WE Ch. 5.4 - Prob. 30WE Ch. 5.4 - Prob. 31WE Ch. 5.4 - Prob. 32WE Ch. 5.4 - Prob. 33WE Ch. 5.4 - Prob. 34WE Ch. 5.4 - Prob. 35WE Ch. 5.4 - Prob. 36WE Ch. 5.4 - Prob. 37WE Ch. 5.4 - Prob. 38WE Ch. 5.4 - Prob. 39WE Ch. 5.4 - Prob. 40WE Ch. 5.4 - Prob. 41WE Ch. 5.4 - Prob. 42WE Ch. 5.4 - Prob. 43WE Ch. 5.4 - Prob. 1E Ch. 5.4 - Prob. 2E Ch. 5.4 - Prob. 3E Ch. 5.4 - Prob. 4E Ch. 5.4 - Prob. 5E Ch. 5.4 - Prob. 6E Ch. 5.4 - Prob. 7E Ch. 5.4 - Prob. 8E Ch. 5.4 - Prob. 9E Ch. 5.4 - Prob. 10E Ch. 5.4 - Prob. 11E Ch. 5.4 - Prob. 12E Ch. 5.5 - Prob. 1OE Ch. 5.5 - Prob. 2OE Ch. 5.5 - Prob. 3OE Ch. 5.5 - Prob. 4OE Ch. 5.5 - Prob. 5OE Ch. 5.5 - Prob. 6OE Ch. 5.5 - Prob. 7OE Ch. 5.5 - Prob. 8OE Ch. 5.5 - Prob. 1WE Ch. 5.5 - Prob. 2WE Ch. 5.5 - Prob. 3WE Ch. 5.5 - Prob. 4WE Ch. 5.5 - Prob. 5WE Ch. 5.5 - Prob. 6WE Ch. 5.5 - Prob. 7WE Ch. 5.5 - Prob. 8WE Ch. 5.5 - Prob. 9WE Ch. 5.5 - Prob. 10WE Ch. 5.5 - Prob. 11WE Ch. 5.5 - Prob. 12WE Ch. 5.5 - Prob. 13WE Ch. 5.5 - Prob. 14WE Ch. 5.5 - Prob. 15WE Ch. 5.5 - Prob. 16WE Ch. 5.5 - Prob. 17WE Ch. 5.5 - Prob. 18WE Ch. 5.5 - Prob. 19WE Ch. 5.5 - Prob. 20WE Ch. 5.5 - Prob. 21WE Ch. 5.5 - Prob. 22WE Ch. 5.5 - Prob. 23WE Ch. 5.5 - Prob. 24WE Ch. 5.5 - Prob. 1MRE Ch. 5.5 - Prob. 2MRE Ch. 5.5 - Prob. 3MRE Ch. 5.5 - Prob. 4MRE Ch. 5.5 - Prob. 5MRE Ch. 5.5 - Prob. 6MRE Ch. 5.5 - Prob. 7MRE Ch. 5.5 - Prob. 8MRE Ch. 5.5 - Prob. 9MRE Ch. 5.5 - Prob. 10MRE Ch. 5.5 - Prob. 11MRE Ch. 5.5 - Prob. 12MRE Ch. 5.6 - Prob. 1OE Ch. 5.6 - Prob. 2OE Ch. 5.6 - Prob. 3OE Ch. 5.6 - Prob. 4OE Ch. 5.6 - Prob. 5OE Ch. 5.6 - Prob. 6OE Ch. 5.6 - Prob. 7OE Ch. 5.6 - Prob. 8OE Ch. 5.6 - Prob. 1WE Ch. 5.6 - Prob. 2WE Ch. 5.6 - Prob. 3WE Ch. 5.6 - Prob. 4WE Ch. 5.6 - Prob. 5WE Ch. 5.6 - Prob. 6WE Ch. 5.6 - Prob. 7WE Ch. 5.6 - Prob. 8WE Ch. 5.6 - Prob. 9WE Ch. 5.6 - Prob. 10WE Ch. 5.6 - Prob. 11WE Ch. 5.6 - Prob. 12WE Ch. 5.6 - Prob. 13WE Ch. 5.6 - Prob. 14WE Ch. 5.6 - Prob. 15WE Ch. 5.6 - 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Prob. 24WE Ch. 5.7 - Prob. 25WE Ch. 5.7 - Prob. 26WE Ch. 5.7 - Prob. 27WE Ch. 5.7 - Prob. 28WE Ch. 5.7 - Prob. 29WE Ch. 5.7 - Prob. 30WE Ch. 5.7 - Prob. 31WE Ch. 5.7 - Prob. 32WE Ch. 5.7 - Prob. 33WE Ch. 5.7 - Prob. 34WE Ch. 5.7 - Prob. 35WE Ch. 5.7 - Prob. 1MRE Ch. 5.7 - Prob. 2MRE Ch. 5.7 - Prob. 3MRE Ch. 5.7 - Prob. 4MRE Ch. 5.7 - Prob. 5MRE Ch. 5.7 - Prob. 6MRE Ch. 5.7 - Prob. 7MRE Ch. 5.7 - Prob. 8MRE Ch. 5.7 - Prob. 9MRE Ch. 5.7 - Prob. 10MRE Ch. 5.7 - Prob. 11MRE Ch. 5.7 - Prob. 12MRE Ch. 5.7 - Prob. 1ST Ch. 5.7 - Prob. 2ST Ch. 5.7 - Prob. 3ST Ch. 5.7 - Prob. 4ST Ch. 5.7 - Prob. 5ST Ch. 5.7 - Prob. 6ST Ch. 5.7 - Prob. 7ST Ch. 5.7 - Prob. 8ST Ch. 5.8 - Prob. 1OE Ch. 5.8 - Prob. 2OE Ch. 5.8 - Prob. 3OE Ch. 5.8 - Prob. 4OE Ch. 5.8 - Prob. 5OE Ch. 5.8 - Prob. 6OE Ch. 5.8 - Prob. 7OE Ch. 5.8 - Prob. 8OE Ch. 5.8 - Prob. 9OE Ch. 5.8 - Prob. 1WE Ch. 5.8 - Prob. 2WE Ch. 5.8 - Prob. 3WE Ch. 5.8 - Prob. 4WE Ch. 5.8 - Prob. 5WE Ch. 5.8 - Prob. 6WE Ch. 5.8 - Prob. 7WE Ch. 5.8 - Prob. 8WE Ch. 5.8 - 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