SOLVEa'a33. (a)(b) (a’a*)'(c)a34. (a)(b) (2a’a*)*(c) (-3z*)'(2:")

Answered: SOLVE a'a 33. (a) (b) (a’a*)' (c) a 34.…

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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Question

SOLVE
a'a
33. (a)
(b) (a’a*)'
(c)
a
34. (a)
(b) (2a’a*)*
(c) (-3z*)'(2:")

Expert Solution

Step 1

Hello. Since your question has multiple parts, we will solve first question for you. If you want remaining sub-parts to be solved, then please resubmit the whole question and specify those sub-parts you want us to solve.

(a)

Given that:

$\frac{a^{9} a^{- 2}}{a}$

To apply exponent property: $a^{m} \cdot a^{n} = a^{m + n} a n d \frac{a^{m}}{a^{n}} = a^{m - n}$

To solve:

$\begin{matrix} \frac{a^{9} a^{- 2}}{a} = \frac{a^{9 + (- 2)}}{a} \\ = \frac{a^{9 - 2}}{a} \\ = \frac{a^{7}}{a} \\ = a^{7 - 1} \\ = a^{6} \\ H e n c e, \frac{a^{9} a^{- 2}}{a} = a^{6} \end{matrix}$

Step 2

(b)

Given that:

${(a^{2} a^{4})}^{3}$

To solve:

$\begin{matrix} {(a^{2} a^{4})}^{3} = {(a^{2 + 4})}^{3} \\ = {(a^{6})}^{3} \\ = a^{6 \times 3} since, {(a^{m})}^{n} = a^{m \times n} \\ = a^{18} \end{matrix}$