College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.2 - Page 33: 110



Work Step by Step

$$(3x^{-4}yz^{-7})(3x)^{-3}$$ When a product is raised to an exponent, raise each factor to that exponent. $$=(3x^{-4}yz^{-7})(3^{-3}x^{-3})$$ Combine like terms and simplify. $$=(3\times3^{-3})(x^{-4}\times x^{-3})(y)(z^{-7})$$ $$=(3^{(1+(-3)})(x^{-4+(-3)})(y)(z^{-7})$$ $$=(3^{-2})(x^{-7})(y)(z^{-7})$$ When an exponent is negative, write the expression as a fraction and move the base from the numerator to the denominator (or vise versa) and make the exponent positive. $$=\frac{y}{3^{2}x^{7}z^{7}}$$ $$=\frac{y}{9x^{7}z^{7}}$$
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