Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 7 - Exponents and Exponential Functions - 7-3 Multipying Powers with the Same Base - Practice and Problem-Solving Exercises: 45

Answer

$a=-3$ and $b=2$

Work Step by Step

The right hand side (RHS) of the given equation can be equivalently written as : $y^{2} = 1$ X $y^{2} =x^{0}y^{2}$ (since $x^{0} = 1$) Now, $x^{3+a}y^{b} = x^{0}y^{2}$ Comparing the left hand side(LHS) and the right hand side(RHS) of the equation with respect to the exponents of $x$ and $y$,we get : $x^{3+a} = x^{0}$ and $y^{b} = y^{2}$ This implies : 1] $3+a=0$ , hence $3 + a - 3 = 0 - 3$ , hence $a = -3$ 2] $b = 2$ Final result : $a=-3$ and $b=2$
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