Problem 7 Evaluate. $$-4^{0}$$... [FREE SOLUTION]

Chapter 2: Problem 7

Evaluate. $$-4^{0}$$

Short Answer

Expert verified

Using the exponent rule for any non-zero number raised to the power of 0, the expression $-4^0$ evaluates to: $-4^0 = 1$.

Step by step solution

Apply the exponent rule for any non-zero number raised to the power of 0

Since the given expression is $-4^0$, we can simply apply the exponent rule for any non-zero number raised to the power of 0. In this case, we have: $-4^0 = 1$

Write down the final answer

After applying the exponent rule for any non-zero number raised to the power of 0, we found that the expression $-4^0$ evaluates to: \[-4^0 = 1\]

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.

Exponent Rules

When dealing with expressions that include exponents, it is essential to understand the rules that dictate how they function. These rules help simplify expressions and solve problems easily.

Some key rules include:

**Product of Powers Rule**: When you multiply like bases, you add the exponents. For example, $a^m \times a^n = a^{m+n}$.
**Quotient of Powers Rule**: When dividing like bases, subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$.
**Power of a Power Rule**: When raising a power to another power, multiply the exponents: $(a^m)^n = a^{m\times n}$.
**Zero Exponent Rule**: Anything raised to the zero power is 1 (as long as the base is not zero). For example, $a^0 = 1$, where $a eq 0$.

Understanding these rules allows you to manage complex expressions intuitively.
Being consistent with these principles is crucial for evaluating or simplifying any expressions involving exponents.

Zero Exponent

The `Zero Exponent Rule` is one of the critical concepts when dealing with exponents. According to this rule, any non-zero number raised to the power of zero is equal to one.

Here鈥檚 how it works:

Consider a number or variable $a$. If $a$ is non-zero, then $a^0 = 1$.
This rule is powerful because it simplifies expressions effortlessly.
For instance, no matter how big or complex the number might be, if it鈥檚 raised to the zero power, the result is simply 1.

The expression we evaluated, $-4^0$, also follows this rule. So, regardless of the negative sign before the base, the expression simplifies to 1 because $-4$ (taken as the base) to the power of zero is $1$. It's important to note that the zero exponent does not operate on the sign, just the base itself.

Evaluating Expressions

Evaluating expressions is the process of simplifying them to find their value. When working with exponents, the process follows the rules and guidelines set by exponent operations.

In the example of $-4^0$:

We apply the zero exponent rule first. It tells us that any non-zero number raised to zero equals 1.
Thus, even though there is a negative sign in front of the $4^0$, the expression itself ($-4^0$) is interpreted as $-(4^0)$, which becomes $-1\times(1)$.
Applying these rules correctly provides a straightforward outcome: the expression evaluates to $-1$.

Grasping the rules of exponents, including the zero exponent, makes evaluating expressions less challenging. It paves the way for more complicated algebraic manipulations by offering a robust foundation in simpler problems.

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

Evaluate. $$-4^{0}$$

Short Answer

Step by step solution

Apply the exponent rule for any non-zero number raised to the power of 0

Write down the final answer

Key Concepts

Exponent Rules

Zero Exponent

Evaluating Expressions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Geometry

Statistics

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.