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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. 128 (page 521)

In the following exercises, simplify each expression by applying several properties.
$(a) . {(10 k^{4})}^{3} {(5 k^{6})}^{2} (b) . \frac{{(q^{3})}^{6} {(q^{- 2})}^{3}}{{(q^{4})}^{8}}$

Short Answer

Expert verified

The simplified form of the expressions

$(a) . {(10 k^{4})}^{3} {(5 k^{6})}^{2} = 25000 k^{24} (b) . \frac{{(q^{3})}^{6} {(q^{- 2})}^{3}}{{(q^{4})}^{8}} = \frac{1}{q^{20}}$

Step by step solution

01

Part (a) Step 1. Given information.

The given expression is ${(10 k^{4})}^{3} {(5 k^{6})}^{2}$ .

02

Part (a) Step 2. Calculate the expression.

Apply product to a power property

We get, $10^{3} . k^{12} 脳 5^{2} . k^{12}$

$25000 k^{24}$

03

Part (b) Step 1. Given information.

The given expression is $\frac{{(q^{3})}^{6} {(q^{- 2})}^{3}}{{(q^{4})}^{8}}$ .

04

Part (b) Step 2. Calculate the expression.

First of all, apply power property

We get,

$\frac{q^{18} 脳 q^{- 6}}{q^{32}}$

Now, apply the property of the negative exponent and cancel out the common terms

We get,

$\frac{q^{12}}{q^{32}} = \frac{1}{q^{20}} .$

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