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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q.418. (page 560)

Simplify the expression by applying several properties.
$\frac{{(- 3 a^{- 2})}^{4} {(2 a^{4})}^{2}}{{(- 6 a^{2})}^{3}}$

Short Answer

Expert verified

The solution is $\frac{3}{- 2 a^{6}}$ .

Step by step solution

01

Step 1. Given information.

The given expression is $\frac{{(- 3 a^{- 2})}^{4} {(2 a^{4})}^{2}}{{(- 6 a^{2})}^{3}}$ .

02

Step 2. Simplify the expression.

Solve it as follows:

$\frac{{(- 3 a^{- 2})}^{4} {(2 a^{4})}^{2}}{{(- 6 a^{2})}^{3}} = \frac{{(- 3)}^{4} {(a^{- 2})}^{4} {(2)}^{2} {(a^{4})}^{2}}{{(- 6)}^{3} {(a^{2})}^{3}} \frac{{(- 3 a^{- 2})}^{4} {(2 a^{4})}^{2}}{{(- 6 a^{2})}^{3}} = \frac{81 a^{- 8} 路 4 路 a^{8}}{- 216 a^{6}} \frac{{(- 3 a^{- 2})}^{4} {(2 a^{4})}^{2}}{{(- 6 a^{2})}^{3}} = \frac{324 a^{8 - 8}}{- 216 a^{6}} \frac{{(- 3 a^{- 2})}^{4} {(2 a^{4})}^{2}}{{(- 6 a^{2})}^{3}} = \frac{324 a^{0}}{- 216 a^{6}} \frac{{(- 3 a^{- 2})}^{4} {(2 a^{4})}^{2}}{{(- 6 a^{2})}^{3}} = \frac{3}{- 2 a^{6}}$

03

Step 3. Simplified answer.

The simplified expression is $\frac{3}{- 2 a^{6}}$ .

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