Chapter 5: Q. 5.24 (page 503)

Simplify each expression:
$ⓐ x^{12} \cdot x^{4} ⓑ 10 \cdot 10^{x} ⓒ 2 z \cdot 6 z^{7} ⓓ b^{5} \cdot b^{9} \cdot b^{5}$

Short Answer

Expert verified

The simplified expression of $x^{12} \cdot x^{4} = x^{16}$

The simplified expression of $10 \cdot 10^{x} = 10^{1 + x}$

The simplified expression of $2 z \cdot 6 z^{7} = 2 z^{8}$

The simplified expression of $b^{5} \cdot b^{9} \cdot b^{5} = b^{19}$

Step by step solution

Step 1. Given Information

In the given question we have to simplify each expression:

$ⓐ x^{12} \cdot x^{4} ⓑ 10 \cdot 10^{x} ⓒ 2 z \cdot 6 z^{7} ⓓ b^{5} \cdot b^{9} \cdot b^{5}$

Part(a) Step 1. Simplifying the expression x12·x4

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

Part(a) Step 2. The given expression is x12·x4

Add the exponents, since bases are the same.

$x^{12} \cdot x^{4} = x^{12 + 4}$

Simplifying the expression.

$x^{12} \cdot x^{4} = x^{16}$

Part(b) Step 1. Simplifying the expression 10·10x

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

Part(b) Step 2. The given expression is 10·10x

Rewrite $a = a^{1}$

$10 \cdot 10^{x} = 10^{1} \cdot 10^{x}$

Add the exponents, since bases are the same.

localid="1644685692508" $10 \cdot 10^{x} = 10^{1 + x}$

Part(c) Step 1. Simplifying the expression 2z·6z7

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

Part(c) Step 2. The given expression is 2z·6z7

Rewrite $a = a^{1}$

$2 z \cdot 6 z^{7} = 2 z^{1} \cdot 6 z^{7}$

Use the Commutative Property and use the Product Property

$2 z \cdot 6 z^{7} = 2 \cdot 6 z^{1 + 7}$

Simplifying the expression.

$2 z \cdot 6 z^{7} = 2 z^{8}$

Part(d) Step 1. Simplifying the expression b5·b9·b5

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

Part(d) Step 2. The given expression is b5·b9·b5

Add the exponents, since bases are the same.

$b^{5} \cdot b^{9} \cdot b^{5} = b^{5 + 9 + 5}$

Simplifying the expression.

$b^{5} \cdot b^{9} \cdot b^{5} = b^{19}$

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Simplify each expression:
$ⓐ x^{12} \cdot x^{4} ⓑ 10 \cdot 10^{x} ⓒ 2 z \cdot 6 z^{7} ⓓ b^{5} \cdot b^{9} \cdot b^{5}$

Short Answer

Step by step solution

Step 1. Given Information

Part(a) Step 1. Simplifying the expression x12·x4

Part(a) Step 2. The given expression is x12·x4

Part(b) Step 1. Simplifying the expression 10·10x

Part(b) Step 2. The given expression is 10·10x

Part(c) Step 1. Simplifying the expression 2z·6z7

Part(c) Step 2. The given expression is 2z·6z7

Part(d) Step 1. Simplifying the expression b5·b9·b5

Part(d) Step 2. The given expression is b5·b9·b5

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Simplify each expression:ⓐx12·x4ⓑ10·10xⓒ2z·6z7ⓓb5·b9·b5

Short Answer

Step by step solution

Step 1. Given Information

Part(a) Step 1. Simplifying the expression x12·x4

Part(a) Step 2. The given expression is x12·x4

Part(b) Step 1. Simplifying the expression 10·10x

Part(b) Step 2. The given expression is 10·10x

Part(c) Step 1. Simplifying the expression 2z·6z7

Part(c) Step 2. The given expression is 2z·6z7

Part(d) Step 1. Simplifying the expression b5·b9·b5

Part(d) Step 2. The given expression is b5·b9·b5

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Mechanics Maths

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Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Simplify each expression:
$ⓐ x^{12} \cdot x^{4} ⓑ 10 \cdot 10^{x} ⓒ 2 z \cdot 6 z^{7} ⓓ b^{5} \cdot b^{9} \cdot b^{5}$