Problem 11 Simplify. $$\left(-\frac{1}{9}... [FREE SOLUTION]

91影视

Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 4: Problem 11

Simplify. $$\left(-\frac{1}{9}\right)^{2}$$

Short Answer

Expert verified

\frac{1}{81}

Step by step solution

Understand the Expression

The expression $\textstyle \big(-\frac{1}{9}\big)^2 $ means that $-\frac{1}{9}$ is being raised to the power of 2. This indicates that we will multiply $-\frac{1}{9}$ by itself.

Multiply the Fractions

Multiply the fraction $-\frac{1}{9}$ by itself: $-\frac{1}{9} \times -\frac{1}{9}$.

Simplify the Multiplication

When multiplying fractions, multiply the numerators together and the denominators together: $\frac{-1 \times -1}{9 \times 9} = \frac{1}{81}$.

Finalize the Result

Since multiplying two negative numbers gives a positive result, the simplified expression is $\frac{1}{81}$.

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.

Simplifying Fractions

Simplifying fractions makes them easier to understand and work with. It involves reducing a fraction to its simplest form.
In our example, we started with $-\frac{1}{9}$.
However, in this exercise, there wasn't much need for simplification.
We kept the fraction as it was until the end. But usually, the steps would be:

Find the greatest common divisor (GCD) of the numerator and the denominator.
Divide both the numerator and the denominator by the GCD.

Always check if both can be divided evenly. This ensures your fraction is in the simplest form.

Multiplication of Fractions

Multiplying fractions is simpler than it seems. You just follow a couple of easy steps.
Here鈥檚 a breakdown:

Multiply numerators: Take the numerators of both fractions and multiply them.
Multiply denominators: Do the same with the denominators.

In our example, we multiplied $-\frac{1}{9}$ by itself:
The numerators: \-1\ times \-1\ is \1\.
The denominators: \9\ times \9\ is \81\.
That gave us \frac{1}{81}\.

Negative Numbers

Negative numbers can sometimes be confusing. But the key rule is that:

Multiplying two negatives: When you multiply two negative numbers, the result is always positive.

In this exercise, when we multiplied $-\frac{1}{9}$ by $-\frac{1}{9}$, we followed this rule:
\-1\ times \-1\ equals \1\, making the fraction positive.
This is why the final expression was \frac{1}{81}\, not \-\frac{1}{81}\.

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. $$\left(-\frac{1}{9}\right)^{2}$$

Short Answer

Step by step solution

Understand the Expression

Multiply the Fractions

Simplify the Multiplication

Finalize the Result

Key Concepts

Simplifying Fractions

Multiplication of Fractions

Negative Numbers

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Applied Mathematics

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.