Chapter 6: Q. 126 (page 711)

In the following exercises, simplify each expression.
$ⓐ {(3 x)}^{2} (5 x) ⓑ {(5 t^{2})}^{3} {(3 t)}^{2}$

Short Answer

Expert verified

(a) The simplified form of the given expression is $45 x^{3}$ .

(b) The simplified form of the given expression is $225 t^{8}$ .

Step by step solution

Step 1. Given Information

In the following exercises, we have to simplify given expression.
$ⓐ {(3 x)}^{2} (5 x) ⓑ {(5 t^{2})}^{3} {(3 t)}^{2}$

Part (a) Step 1. Given expression is (3x)2(5x)

Use the Power Property.

${(3 x)}^{2} (5 x) = {{(3)}^{2} \cdot x}^{2} \cdot 5 \cdot x^{1} {(3 x)}^{2} (5 x) = {9 \cdot x}^{2} \cdot 5 \cdot x^{1}$

Add the exponents.

${(3 x)}^{2} (5 x) = 9 \cdot 5 \cdot x^{1 + 2} {(3 x)}^{2} (5 x) = 45 x^{3}$

Part (b) Step 1. Given expression is (5t2)3(3t)2

Use the Power Property.

${(5 t^{2})}^{3} {(3 t)}^{2} = {{(5)}^{2} \cdot (t^{2})}^{3} {\cdot {(3)}^{2} \cdot (t)}^{2} {(5 t^{2})}^{3} {(3 t)}^{2} = 25 \cdot t^{2 \cdot 3} {\cdot 9 \cdot t}^{2} {(5 t^{2})}^{3} {(3 t)}^{2} = 25 \cdot t^{6} {\cdot 9 \cdot t}^{2}$

Add the exponents.

${(5 t^{2})}^{3} {(3 t)}^{2} = 225 t^{2 + 6} {(5 t^{2})}^{3} {(3 t)}^{2} = 225 t^{8}$

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In the following exercises, simplify each expression.
$ⓐ {(3 x)}^{2} (5 x) ⓑ {(5 t^{2})}^{3} {(3 t)}^{2}$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Given expression is (3x)2(5x)

Part (b) Step 1. Given expression is (5t2)3(3t)2

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In the following exercises, simplify each expression.ⓐ(3x)2(5x)ⓑ(5t2)3(3t)2

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Given expression is (3x)2(5x)

Part (b) Step 1. Given expression is (5t2)3(3t)2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each expression.
$ⓐ {(3 x)}^{2} (5 x) ⓑ {(5 t^{2})}^{3} {(3 t)}^{2}$