Problem 17 Simplify. Write answers with pos... [FREE SOLUTION]

Chapter 15: Problem 17

Simplify. Write answers with positive exponents. $$ x^{5} \cdot x^{8} $$

Short Answer

Expert verified

x^{13}

Step by step solution

- Understand the Properties of Exponents

When multiplying terms with the same base, add their exponents. This is based on the property: $a^m \times a^n = a^{m+n}$.

- Apply the Property

Identify the base and the exponents in the given problem $x^5 \times x^8$. Here, the base is $x$ and the exponents are $5$ and $8$.

- Add the Exponents

Add the exponents together: $5 + 8 = 13$. This gives us $x^{13}$.

- Write the Simplified Expression

The simplified expression is $x^{13}$. Make sure the answer is written with positive exponents.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Multiplying Exponents

Multiplying exponents is a crucial part of mastering algebra. When you see terms with the same base being multiplied, like in the example exercise above, you simply add the exponents together.

For instance, when you have an expression like $x^{5} \times x^{8}$, both terms share the same base, which is $x$.
According to the rules, you add their exponents together:

$a^m \times a^n = a^{m+n}$

So, for our exercise, it will be: $x^{5} \times x^{8} = x^{5+8} = x^{13}$.
This makes multiplying exponents with the same base a straightforward task!

Simplifying Expressions

Simplifying expressions is about making them look as clean and straightforward as possible. It often involves using the properties of exponents to combine like terms.
Let's look at our previous example again: $x^{5} \times x^{8}$.
Here, combining the exponents is necessary to simplify the expression.

By adding 5 and 8 together, we get $x^{13}$.
This process of combining and reducing exponents helps to manage and work with the expressions easier.

Moreover, simplifying expressions also ensures the answer is in the most understandable format, which is essential in mathematics.

Positive Exponents

When it comes to simplifying expressions, it's important to ensure all exponents in the final answer are positive.
In our example $x^{5} \times x^{8}$, we end up with $x^{13}$. Fortunately, 13 is already positive.

However, if you ever find yourself with negative exponents after simplifying, remember the rule:

To convert a negative exponent into a positive exponent, you can take the reciprocal of the base.
For example, $a^{-n} = \frac{1}{a^n}$.

This ensures your final expression is always presented in the simplest and most standard form.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Simplify. Write answers with positive exponents. $$ x^{5} \cdot x^{8} $$

Short Answer

Step by step solution

- Understand the Properties of Exponents

- Apply the Property

- Add the Exponents

- Write the Simplified Expression

Key Concepts

Multiplying Exponents

Simplifying Expressions

Positive Exponents

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Calculus

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.