Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Chapter 4: Problem 12
If \(c=-1 / 5\), evaluate \(-c^{2}\).
Short Answer
Expert verified
The value of \(-c^2\) is \(-\frac{1}{25}\).
Step by step solution
01
Understand the Expression
The expression we need to evaluate is \(-c^2\). This means that we first need to square the value of \(c\) and then multiply the result by \(-1\).
02
Substitute the Value of \(c\)
The problem states that \(c = -\frac{1}{5}\). Substitute this value into the expression, giving us \(-(-\frac{1}{5})^2\).
03
Square the Value of \(c\)
Carry out the squaring operation: \((-\frac{1}{5})^2 = (-1)^2 \times (\frac{1}{5})^2 = 1 \times \frac{1}{25} = \frac{1}{25}\).
04
Apply the Negative Sign
Finally, apply the negative sign outside the squared value:\(-c^2 = -\frac{1}{25}\).
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.
Negative Numbers
Negative numbers are numbers that are less than zero. They have a minus sign (-) in front of them. These numbers can be found on the left side of the number line.
For example,
For example,
- -1
- -3.5
- -10
- Addition: Adding a negative number is like subtracting its absolute value. For instance, 5 + (-3) = 5 - 3 = 2.
- Subtraction: Subtracting a negative number is the same as adding its absolute value. For example, 5 - (-3) = 5 + 3 = 8.
- Multiplication: Multiplying two negative numbers results in a positive product. For instance, (-2) x (-3) = 6.
- Division: Dividing two negative numbers also results in a positive quotient. For example, (-6) / (-3) = 2.
Exponents
Exponents are a way to express repeated multiplication of the same number. For example, 3 squared (written as \(3^2\)) means 3 multiplied by itself: 3 x 3. The small number, known as the exponent, tells you how many times to use the base as a factor. Here's a quick breakdown of basic exponent rules:
- Power of zero: Any non-zero number raised to the power of zero equals one. For example, \(5^0 = 1\).
- Power of one: Any number raised to the power of one is the number itself. For example, \(7^1 = 7\).
- Multiplication of same bases: When multiplying like bases, you add the exponents. For example, \(x^a \times x^b = x^{a+b}\).
- Division of same bases: When dividing like bases, you subtract the exponents. For example, \(x^a / x^b = x^{a-b}\).
- Since 2 is even, \((-2)^2 = 4\).
- Since 3 is odd, \((-2)^3 = -8\).
Substitution Method
The substitution method is a technique in algebra used to replace a variable with its known value in an expression or equation. This method simplifies calculations and allows you to solve for other unknowns easily. Here's how it works:
- Identify the variable and its given value in the problem. For example, if you know \(x = 3\), you can substitute 3 for any occurrence of \(x\) in an equation.
- Rewrite the original expression or equation with the substituted value. This step reduces the problem to numerical calculations, removing the variable.
- Perform the arithmetic operations to solve the expression or equation. With the variable substituted, you can solve for the remaining unknowns or evaluate the expression.
