College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Section 1.6 - Other Types of Equations and Applications - 1.6 Exercises - Page 136: 98

Answer

$y=\pm(a^{2/3}-x^{2/3})^{3/2}$

Work Step by Step

We solve this equation for $y$: $x^{2/3}+y^{2/3}=a^{2/3}$ $y^{2/3}=a^{2/3}-x^{2/3}$ We cube both sides: $(y^{2/3})^{3}=(a^{2/3}-x^{2/3})^{3}$ $y^{2*3/3}=a^{2*3/3}-x^{2*3/3}$ $y^{2}=(a^{2/3}-x^{2/3})^{3}$ We take the square root of both sides: $y=\pm\sqrt{(a^{2/3}-x^{2/3})^{3}}$ $y=\pm(a^{2/3}-x^{2/3})^{3/2}$
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