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Evaluate each expression. See Example 2. 10. 16¹/2

Evaluate each expression. See Example 2. 10. 16¹/2

Algebra and Trigonometry (6th Edition)
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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Please explain each step, like which rule you're using I also attached the example kindly take a look
Evaluate each expression. See Example 2. 10. 16¹/2
Transcribed Image Text:Evaluate each expression. See Example 2. 10. 16¹/2
# 98. (-27x) 1/3 For this first expression, we need the Power of a Power Rule to multiply the exponents. The basic form is: (ar)s = ars So we get: (-27x)/3-270*1/3x91/3) First, we look at the number and exponent in front of the variable x. -2701-1/3) is -27(1/3) and can also be written as the cubic root: -³√(27) We can see that the principal third root of 27 is 3, which is an odd root: -³√(3*3*3) = -³√(3³) Therefore, we get -3 as a result. Then we ook at the variable x and its exponent. X(9*1/3) = x³ Since the exponent is positive, we do not need a reciprocal of the base number and the exponent. If we put everything together, we get the result: -3x³ The expression did not require us to multiply the same variables with different exponents, so we did not need the Product Rule, and we also did not need the Power of the Product Rule since there is only one variable. Since we did not have fractions, we also did not need the Quotient Rule or the Power to the Quotient Rule. #30. V(5)* √(7) For the second expression, we multiply radicals with the same index, so we apply the Product Rule. We can then write the expression like this: V(5*7) = V(35) The expression cannot be simplified, so the result is V35
Transcribed Image Text:# 98. (-27x) 1/3 For this first expression, we need the Power of a Power Rule to multiply the exponents. The basic form is: (ar)s = ars So we get: (-27x)/3-270*1/3x91/3) First, we look at the number and exponent in front of the variable x. -2701-1/3) is -27(1/3) and can also be written as the cubic root: -³√(27) We can see that the principal third root of 27 is 3, which is an odd root: -³√(3*3*3) = -³√(3³) Therefore, we get -3 as a result. Then we ook at the variable x and its exponent. X(9*1/3) = x³ Since the exponent is positive, we do not need a reciprocal of the base number and the exponent. If we put everything together, we get the result: -3x³ The expression did not require us to multiply the same variables with different exponents, so we did not need the Product Rule, and we also did not need the Power of the Product Rule since there is only one variable. Since we did not have fractions, we also did not need the Quotient Rule or the Power to the Quotient Rule. #30. V(5)* √(7) For the second expression, we multiply radicals with the same index, so we apply the Product Rule. We can then write the expression like this: V(5*7) = V(35) The expression cannot be simplified, so the result is V35
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