Chapter 5: Q. 5.23 (page 502)

Simplify each expression:
$ⓐ b^{9} \cdot b^{8} ⓑ 4^{2 x} \cdot 4^{x} ⓒ 3 p^{5} \cdot 4 p ⓓ x^{6} \cdot x^{4} \cdot x^{8}$

Short Answer

Expert verified

The simplified expression of $b^{9} \cdot b^{8} = b^{17}$ .

The simplified expression of $4^{2 x} \cdot 4^{x} = 4^{3 x}$

The simplified expression of $3 p^{5} \cdot 4 p = 12 p^{6}$

The simplified expression of $x^{6} \cdot x^{4} \cdot x^{8} = x^{18}$

Step by step solution

Step 1. Given Information

In the given question we have to simplify each expression:

ⓐ b^{9} \cdot b^{8} ⓑ 4^{2 x} \cdot 4^{x} ⓒ 3 p^{5} \cdot 4 p ⓓ x^{6} \cdot x^{4} \cdot x^{8}

Part(a) Step 1. Simplifying the expression b9·b8.

As we know $a^{m} \cdot a^{n} = a^{m + n}$

Part(a) Step 2. The given expression is b9·b8.

Add the exponents, since bases are the same.

$b^{9} \cdot b^{8} = b^{9 + 8}$

Simplifying the expression.

$b^{9} \cdot b^{8} = b^{17}$

Part(b) Step 1. Simplifying the expression 42x·4x

As we know $a^{m} \cdot a^{n} = a^{m + n}$

Part(b) Step 2. The given expression is 42x·4x

Add the exponents, since bases are the same.

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

Simplifying the expression.

$4^{2 x} \cdot 4^{x} = 4^{3 x}$

Part(c) Step 1. Simplifying the expression 3p5·4p

As we know $a^{m} \cdot a^{n} = a^{m + n}$

Part(c) Step 2. The given expression is 3p5·4p

Rewrite, $a = a^{1}$

$3 p^{5} \cdot 4 p = 3 p^{5} \cdot 4 p^{1}$

Use the Commutative Property and use the Product Property

$3 p^{5} \cdot 4 p = 3 \cdot 4 \cdot p^{5} \cdot p^{1} 3 p^{5} \cdot 4 p = 3 \cdot 4 \cdot p^{5 + 1}$

Simplifying the expression.

$3 p^{5} \cdot 4 p = 12 p^{6}$

Part(d) Step 1. Simplifying the expression x6·x4·x8

As we know $a^{m} \cdot a^{n} = a^{m + n}$

Part(d) Step 2. The given expression is x6·x4·x8

Add the exponents, since bases are the same.

$x^{6} \cdot x^{4} \cdot x^{8} = x^{6 + 4 + 8}$

Simplifying the expression.

$x^{6} \cdot x^{4} \cdot x^{8} = x^{18}$

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Simplify each expression:
$ⓐ b^{9} \cdot b^{8} ⓑ 4^{2 x} \cdot 4^{x} ⓒ 3 p^{5} \cdot 4 p ⓓ x^{6} \cdot x^{4} \cdot x^{8}$

Short Answer

Step by step solution

Step 1. Given Information

Part(a) Step 1. Simplifying the expression b9·b8.

Part(a) Step 2. The given expression is b9·b8.

Part(b) Step 1. Simplifying the expression 42x·4x

Part(b) Step 2. The given expression is 42x·4x

Part(c) Step 1. Simplifying the expression 3p5·4p

Part(c) Step 2. The given expression is 3p5·4p

Part(d) Step 1. Simplifying the expression x6·x4·x8

Part(d) Step 2. The given expression is x6·x4·x8

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Simplify each expression:ⓐb9·b8ⓑ42x·4xⓒ3p5·4pⓓx6·x4·x8

Short Answer

Step by step solution

Step 1. Given Information

Part(a) Step 1. Simplifying the expression b9·b8.

Part(a) Step 2. The given expression is b9·b8.

Part(b) Step 1. Simplifying the expression 42x·4x

Part(b) Step 2. The given expression is 42x·4x

Part(c) Step 1. Simplifying the expression 3p5·4p

Part(c) Step 2. The given expression is 3p5·4p

Part(d) Step 1. Simplifying the expression x6·x4·x8

Part(d) Step 2. The given expression is x6·x4·x8

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

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Study anywhere. Anytime. Across all devices.

Simplify each expression:
$ⓐ b^{9} \cdot b^{8} ⓑ 4^{2 x} \cdot 4^{x} ⓒ 3 p^{5} \cdot 4 p ⓓ x^{6} \cdot x^{4} \cdot x^{8}$