Chapter 5: Q. 82. (page 520)

In the following exercises, simplify each expression using the properties for exponents.
$ⓐ x^{4} \cdot x^{2} ⓑ 8^{9 x} \cdot 8^{3} ⓒ 3 z^{25} \cdot 5 z^{8} ⓓ y \cdot y^{3} \cdot y^{5}$

Short Answer

Expert verified

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

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

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

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

Step by step solution

Step 1. Given Information

In the given question we have to simplify the given expression:
$ⓐ x^{4} \cdot x^{2} ⓑ 8^{9 x} \cdot 8^{3} ⓒ 3 z^{25} \cdot 5 z^{8} ⓓ y \cdot y^{3} \cdot y^{5}$

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

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

$x^{4} \cdot x^{2} = x^{4 + 2}$

Simplify.

$x^{4} \cdot x^{2} = x^{6}$

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

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

$8^{9 x} \cdot 8^{3} = 8^{9 x + 3}$

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

$3 z^{25} \cdot 5 z^{8} = 3 \cdot 5 \cdot z^{25} \cdot z^{8}$

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

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

Simplify.

$3 z^{25} \cdot 5 z^{8} = 15 z^{33}$

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

$y \cdot y^{3} \cdot y^{5} = y^{1} \cdot y^{3} \cdot y^{5}$

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

$y \cdot y^{3} \cdot y^{5} = y^{1 + 3 + 5}$

Simplify.

$y \cdot y^{3} \cdot y^{5} = y^{9}$

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In the following exercises, simplify each expression using the properties for exponents.
$ⓐ x^{4} \cdot x^{2} ⓑ 8^{9 x} \cdot 8^{3} ⓒ 3 z^{25} \cdot 5 z^{8} ⓓ y \cdot y^{3} \cdot y^{5}$

Short Answer

Step by step solution

Step 1. Given Information

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

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

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

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

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In the following exercises, simplify each expression using the properties for exponents.ⓐx4·x2ⓑ89x·83ⓒ3z25·5z8ⓓy·y3·y5

Short Answer

Step by step solution

Step 1. Given Information

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

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

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

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Applied Mathematics

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Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each expression using the properties for exponents.
$ⓐ x^{4} \cdot x^{2} ⓑ 8^{9 x} \cdot 8^{3} ⓒ 3 z^{25} \cdot 5 z^{8} ⓓ y \cdot y^{3} \cdot y^{5}$