Q. 188 In the following exercises, simp... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 188 (page 798)

In the following exercises, simplify.
a. $(3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}})$
b. $(- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}})$

Short Answer

Expert verified

On multiplication, we get $63 x^{2} \sqrt{4 x}, 60 a \sqrt[3]{5 a^{2}}$ respectively

Step by step solution

Part (a) Step 1: Given information

Given the expression $(3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}}), (- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}})$

Part (a) Step 2: Multiplying the terms and simplifying

Multiplying the terms and simplifying, we get

$(3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}}) = (3 路 7) (\sqrt{2 x^{3}} 路 \sqrt{18 x^{2}}) (3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}}) = 21 路 \sqrt{36 x^{5}} (3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}}) = 21 路 \sqrt{9 x^{4} 路 4 x} (3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}}) = 21 路 \sqrt{9 x^{4}} 路 \sqrt{4 x} (3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}}) = 21 路 \sqrt{{(3 x^{2})}^{2}} 路 \sqrt{4 x} (3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}}) = 21 路 3 x^{2} 路 \sqrt{4 x} (3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}}) = 63 x^{2} \sqrt{4 x}$

Part (b) Step 1: Given information

Given expression $(- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}})$

Part (b) Step 2: Multiplying the terms and simplifying

Simplifying, we get

$(- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}}) = [(- 6) 路 (- 2)] (\sqrt[3]{20 a^{2}} . \sqrt[3]{16 a^{3}}) (- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}}) = 12 路 \sqrt[3]{320 a^{5}} (- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}}) = 12 路 \sqrt[3]{64 a^{3} 路 5 a^{2}} (- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}}) = 12 路 \sqrt[3]{64 a^{3}} 路 \sqrt[3]{5 a^{2}} (- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}}) = 12 路 \sqrt[3]{(4 a)^{3}} 路 \sqrt[3]{5 a^{2}} (- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}}) = 15 路 4 a 路 \sqrt[3]{5 a^{2}} (- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}}) = 60 a \sqrt[3]{5 a^{2}}$

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91影视

In the following exercises, simplify.
a. $(3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}})$
b. $(- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}})$

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Multiplying the terms and simplifying

Part (b) Step 1: Given information

Part (b) Step 2: Multiplying the terms and simplifying

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91影视

In the following exercises, simplify.a.32x3718x2b.-620a23-216a33

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Multiplying the terms and simplifying

Part (b) Step 1: Given information

Part (b) Step 2: Multiplying the terms and simplifying

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
a. $(3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}})$
b. $(- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}})$