Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 3 - Exponents, Polynomials and Functions - 3.1 Rules for Exponents - 3.1 Exercises: 73

Answer

$(4m^{3}n^{6}p^{2})^{\frac{1}{7}}=4^{\frac{1}{7}}m^{\frac{3}{7}}n^{\frac{6}{7}}p^{\frac{2}{7}}$

Work Step by Step

Step 1: The index of the radical is 7, so the denominator of the fractional exponent is 7. Step 2: Therefore, the expression is written as $(4m^{3}n^{6}p^{2})^{\frac{1}{7}}$. Step 3: $(4m^{3}n^{6}p^{2})^{\frac{1}{7}}=4^{\frac{1}{7}}m^{\frac{3}{7}}n^{\frac{6}{7}}p^{\frac{2}{7}}$
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