Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Prerequisites - Review Exercises - Page 62: 35


Part A: $a^{2}b^{2}$ Part B: $3a^{3}b^{2}$

Work Step by Step

Note: $a^{n}a^{m} = a^{n + m}$ Note: $\frac{a^{n}}{a^{m}}$ = $a^{n-m}$ Note: $a^{0} = 1$ Part A: The problem can be rewritten as: $\frac{a^{2}b^{0}}{b^{-2}}$ since $b^{0} = 1$ To eliminate the negative exponent the b components can be simplified: $\frac{b^{0}}{b^{-2}}$ = $b^{0 - (-2)}$ = $b^{2}$ Therefore, the problem simplifies to: $a^{2}b^{2}$ Part B: Using the first note: $(a^{2}b^{4})(3ab^{-2})$ = $3a^{2 + 1}b^{4 + (-2)}$ = $3a^{3}b^{2}$
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