Chapter 7: Q66. (page 406)

Write three different expressions that can be simplified to $x^{6}$ .

Short Answer

Expert verified

The three different expressions that can be simplified as $x^{6}$ are

$x^{2} \times x^{4}, x^{3} \times x^{3}, and x \times x^{5}$

Step by step solution

Step 1. State the multiplication rule of laws of indices.

If the two terms have the same base (in this case x) and are to be multiplied together their indices are added.

In general: $x^{m} \times x^{n} = x^{m + n}$

Step 2. Find the three different additions in which number 6 will be obtained.

The number 6 can be obtained in the following three different ways.

$\begin{array}{l} 2 + 4 = 6 \\ 3 + 3 = 6 \\ 1 + 5 = 6 \end{array}$

Step 3. Find the required expression.

Using the multiplication rule of indices the three different expression that can be simplified to $x^{6}$ are as follows.

$x^{6} = x^{2 + 4} = x^{2} \times x^{4} x^{6} = x^{3 + 3} = x^{3} \times x^{30} x^{6} = x^{1 + 5} = x^{1} \times x^{5} = x \times x^{5} [x^{1} = x]$

Therefore, the required expression are $x^{2} \times x^{4}, x^{3} \times x^{3} and x \times x^{5} .$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Write three different expressions that can be simplified to $x^{6}$ .

Short Answer

Step by step solution

Step 1. State the multiplication rule of laws of indices.

Step 2. Find the three different additions in which number 6 will be obtained.

Step 3. Find the required expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Geometry

Logic and Functions

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Write three different expressions that can be simplified tox6.

Short Answer

Step by step solution

Step 1. State the multiplication rule of laws of indices.

Step 2. Find the three different additions in which number 6 will be obtained.

Step 3. Find the required expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Geometry

Logic and Functions

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Write three different expressions that can be simplified to $x^{6}$ .