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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. 82. (page 520)

In the following exercises, simplify each expression using the properties for exponents.
$鈸� x^{4} 路 x^{2} 鈸� 8^{9 x} 路 8^{3} 鈸� 3 z^{25} 路 5 z^{8} 鈸� y 路 y^{3} 路 y^{5}$

Short Answer

Expert verified

The simplified form of given expression $x^{4} 路 x^{2} = x^{6}$

The simplified form of given expression $8^{9 x} 路 8^{3} = 8^{9 x + 3}$

The simplified form of given expression $3 z^{25} 路 5 z^{8} = 15 z^{33}$

The simplified form of given expression $y 路 y^{3} 路 y^{5} = y^{9}$

Step by step solution

01

Step 1. Given Information

In the given question we have to simplify the given expression:
$鈸� x^{4} 路 x^{2} 鈸� 8^{9 x} 路 8^{3} 鈸� 3 z^{25} 路 5 z^{8} 鈸� y 路 y^{3} 路 y^{5}$

02

Part (a) Step 1. The given expression is x4·x2

Use the Product Property, $a^{m} 路 a^{n} = a^{m + n}$

$x^{4} 路 x^{2} = x^{4 + 2}$

Simplify.

$x^{4} 路 x^{2} = x^{6}$

03

Part (b) Step 1. The given expression is 89x·83

Use the Product Property, $a^{m} 路 a^{n} = a^{m + n}$

$8^{9 x} 路 8^{3} = 8^{9 x + 3}$

04

Part (c) Step 1. The given expression is 3z25·5z8

$3 z^{25} 路 5 z^{8} = 3 路 5 路 z^{25} 路 z^{8}$

Use the Product Property, $a^{m} 路 a^{n} = a^{m + n}$

$3 z^{25} 路 5 z^{8} = 15 路 z^{25 + 8}$

Simplify.

$3 z^{25} 路 5 z^{8} = 15 z^{33}$

05

Part (d) Step 1. The given expression is y·y3·y5

$y 路 y^{3} 路 y^{5} = y^{1} 路 y^{3} 路 y^{5}$

Use the Product Property, $a^{m} 路 a^{n} = a^{m + n}$

$y 路 y^{3} 路 y^{5} = y^{1 + 3 + 5}$

Simplify.

$y 路 y^{3} 路 y^{5} = y^{9}$

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Most popular questions from this chapter

Multiply each pair of conjugates using the product of the conjugates pattern.

$(a b - 4) (a b + 4)$

Multiply each pair of conjugates using the product of the conjugates pattern.

$(5 k + 6) (5 k - 6)$

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(b) $(\frac{2}{5} a^{4} b^{3}) (15 a b^{3})$ .

Find the product of the below expression.

$(p - 3) (p + 3)$

Multiply each pair of conjugates using the product of the conjugates pattern.

$(15 m^{2} - 8 n^{4}) (15 m^{2} + 8 n^{4})$

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