Problem 235 In the following exercises, simp... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 10: Problem 235

In the following exercises, simplify. $$-7^{0}$$

Short Answer

Expert verified

The simplified expression is $-1$.

Step by step solution

Understand exponent rules

Recall that any number raised to the power of zero is equal to 1. This is known as the zero exponent rule. Mathematically, for any non-zero number a, $a^0 = 1$.

Apply the zero exponent rule

Apply the zero exponent rule to the given expression. Here, the expression is $-7^0$. Using the rule, replace $7^0$ with 1.

Simplify the expression

Since $7^0 = 1$, the original expression $-7^0$ simplifies to $-1$.

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.

zero exponent rule

One of the fundamental rules in the study of exponents is the zero exponent rule. This rule states that any non-zero number raised to the power of zero equals 1. In mathematical terms, if we have a non-zero number represented as 'a', then the rule can be written as $a^0 = 1$. This rule is essential to understand and is frequently used in various mathematical problems. The intuition behind this rule is related to decreasing the exponent: as we decrease the exponent by one, we divide the base by itself when the exponent hits zero, leaving us with 1. Hence, $7^0$ simplifies to 1. Knowing and remembering this rule helps in simplifying more complex expressions involving exponents.

exponents

Exponents are a way to express repeated multiplication of a number by itself. For instance, in the expression $3^4$, the number 3 is the base, and the number 4 is the exponent. This means 3 is multiplied by itself 4 times: $3 \times 3 \times 3 \times 3$. Exponents follow specific rules that help simplify expressions including:

Product of Powers Rule: $a^m \times a^n = a^{m+n}$
Power of a Power Rule: $(a^m)^n = a^{mn}$
Quotient of Powers Rule: $\frac{a^m}{a^n} = a^{m-n}$ for $a eq 0$

These rules are crucial for combining and breaking down expressions involving exponents.

negative numbers

Negative numbers are numbers less than zero, represented with a minus sign such as -1, -2, -3, etc. When dealing with exponents and negative numbers, we need to be mindful of the signs. For example, in the exercise $-7^0$, we can see two parts: the negative sign and the exponentiation. According to the zero exponent rule, $7^0$ simplifies to 1. Thus, $-7^0$ becomes $-1$. This indicates that while exponents have specific rules, the ordinary rules of arithmetic, such as handling negative signs, still apply. Always carefully look at the context where negative numbers interact with other operations.

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

In the following exercises, simplify. $$-7^{0}$$

Short Answer

Step by step solution

Understand exponent rules

Apply the zero exponent rule

Simplify the expression

Key Concepts

zero exponent rule

exponents

negative numbers

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Mechanics Maths

Applied Mathematics

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.