Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.2 - Exponents and Scientific Notation - Exercise Set - Page 31: 127


$(-3x^{2})(2x^{-5)}$ is not simplified because the "like terms" have not been combined. The simplified form would be $\frac{-6}{x^{3}}$.

Work Step by Step

1. First, combine the non-variable terms/coefficients. -3 can be multiplied by 2 to give us $-6$. 2. Then, combine the variable terms/powers. Here, the two powers have a common base (x), so to multiply them together, we follow the product rule and add the exponents together: $x^{2} \times x^{-5} = x^{-3}$ 3. Next, because that product left us with a negative exponent, we have to follow the rule for negative exponents: $x^{-3} = \frac{1}{x^{3}}$ 4. Then, we combine the product of our variable terms/powers with the product of our coefficients: $ -6 \times \frac{1}{x^{3}} = \frac{-6}{x^{3}}$.
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