Problem 70 Simplify each expression. $$ ... [FREE SOLUTION]

Chapter 5: Problem 70

Simplify each expression. $$ -3^{0}+4^{0} $$

Short Answer

Expert verified

The simplified expression is 0.

Step by step solution

Understand the Exponent Zero Rule

According to the exponent rules, any non-zero number raised to the power of zero is equal to one. Therefore, both $-3^0$ and $4^0$ simplify to 1. Just remember to treat the negative sign as a separate factor in this context.

Simplify Each Term

Using the exponent zero rule, replace each term with 1. Thus, the expression $-3^0 + 4^0$ becomes $-1 + 1$.

Perform the Addition

Finally, add the simplified terms together: $-1 + 1 = 0$.

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Key Concepts

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

Zero Exponent Rule

The zero exponent rule is a fundamental principle in algebra that often trips up students. It states that any non-zero number raised to the power of zero is always 1. It might seem odd at first, but it's a well-proven rule. Why is this the case? It's all about patterns in powers. For instance, think about \[ 2^3 = 8, \quad 2^2 = 4, \quad 2^1 = 2 \] As the exponent decreases by one, the result is divided by 2 each time. Continuing this pattern to an exponent of zero, \[ 2^0 = \frac{2}{2} = 1 \] This logical sequence shows why any number \[ a^0 = 1 \] as long as $a$ is not zero. In the original exercise, using the zero exponent rule, both $-3^0$ and $4^0$ become 1.

Simplifying Expressions

Simplifying expressions is the process of making algebraic expressions more concise and easier to work with. It involves applying mathematical rules and operations correctly.Key actions include:

Applying exponent rules, such as the zero exponent rule, to simplify powers.
Combining like terms by adding or subtracting where possible.
Performing operations in the correct order (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

For the expression $-3^0 + 4^0$, the zero exponent rule simplifies each term to 1, resulting in $-1 + 1$. This is already a simplified form which is easy to add up.

Algebraic Expressions

Algebraic expressions are combinations of numbers, variables, and arithmetic operations (addition, subtraction, multiplication, and division). They form the basis for much of algebra and allow us to describe real-world situations and solve problems.Some important aspects of dealing with algebraic expressions include:

Understanding the order of operations is crucial to correctly simplifying expressions.
Recognizing and applying rules, like the zero exponent rule, can make working with expressions easier.
Simplified expressions can be used to find unknown values, solve equations, and analyze mathematical relationships.

In the original example, $-3^0 + 4^0$, each component is a term of an algebraic expression. By simplifying it to $-1 + 1$ and then simplifying further to 0, you've effectively managed an algebraic expression!

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91影视

Simplify each expression. $$ -3^{0}+4^{0} $$

Short Answer

Step by step solution

Understand the Exponent Zero Rule

Simplify Each Term

Perform the Addition

Key Concepts

Zero Exponent Rule

Simplifying Expressions

Algebraic Expressions

One App. One Place for Learning.

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