Explanation Definition used: If a > 0 and r is any rational number, then a x = e x ln a . Calculation: The given law of exponents is ( a b ) x = a x b x . So that prove ( a b ) x = a x b x . Consider the left hand side of the given equation. From the above mentioned definition, simplify ( a b ) x as follows. ( a b ) x = e x ( ln a b ) = e x ( ln a + ln b )

Essential Calculus: Early Transcendentals

2nd Edition

ISBN: 9781133112280

Author: James Stewart

Publisher: Cengage Learning

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter C, Problem 9E

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To prove: The law of exponents (ab)x=axbx.

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Chapter C Solutions

Essential Calculus: Early Transcendentals

Ch. C - Prob. 1E Ch. C - Prob. 2E Ch. C - Prob. 3E Ch. C - Prob. 4E Ch. C - Prob. 5E Ch. C - Prob. 6E Ch. C - Prob. 7E Ch. C - Prob. 8E Ch. C - Prob. 9E Ch. C - Prob. 10E

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To prove: The law of exponents ( a b ) x = a x b x .

Solution Summary: The author explains how to prove the fourth law of exponents (ab)x=a

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To prove: The law of exponents (ab)x=axbx.

Chapter C Solutions