Problem 3 Simplify. $$ 4^{0}-4^{1} $... [FREE SOLUTION]

Chapter 15: Problem 3

Simplify. $$ 4^{0}-4^{1} $$

Short Answer

Expert verified

-3

Step by step solution

Understanding Exponent Rules

First, recall the basic exponent rules. Any non-zero number raised to the power of zero is equal to one. Formally, for any non-zero number a, we have a^0 = 1.

Simplify Each Term

Next, simplify each part of the expression. Start with the term 4^0. Using the exponent rule, we get:4^0 = 1.

Simplify the Second Term

Now, simplify the term 4^1. Using the exponent rules, we get:4^1 = 4.

Subtract the Terms

Finally, combine the simplified terms by performing the subtraction:1 - 4 = -3.

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Key Concepts

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

Simplifying Expressions

Simplifying expressions is a fundamental skill in algebra. It involves breaking down more complex expressions into simpler, more comprehensible parts. The goal is to make calculations easier and results clearer.
To simplify an expression, follow these steps:

Understand and apply mathematical rules.
Break down each term of the expression.
Combine like terms and perform basic operations (addition, subtraction, etc.).

For example, in the expression $4^0 - 4^1$, we need to simplify each part individually before combining them. This makes the expression much easier to handle.

Zero Exponent Rule

The Zero Exponent Rule is a key exponent principle, stating that any non-zero number raised to the power of zero is equal to one. Mathematically, for any non-zero number $a$, we have $a^0 = 1$.
This rule can be puzzling, but it鈥檚 built on the consistent pattern of dividing by the base number, progressively reducing the exponent by one each time. Here's a quick demonstration:If you take $4^1$, which equals 4, and divide by the base (4), you get $4^0 = 1$.
This rule simplifies our original expression to: $4^0 - 4^1 = 1 - 4$. This step not only simplifies the expression but also transforms it into a straightforward subtraction problem.

Subtraction of Terms

Subtraction of terms is another essential concept in algebra. Once we simplify each term in an expression, we might end up with a simple subtraction problem. In our exercise of $4^0 - 4^1$, the terms are simplified to $1 - 4$.
Here are some key points to remember when subtracting terms:

Always simplify each term first where possible.
Align terms properly, especially when dealing with variables.
Convert terms to like terms if needed before subtraction.

Our subtraction here is straightforward. We simply perform: $1 - 4 = -3$. We started with a complex expression and by simplifying step by step, we derived an easy-to-understand result.

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91影视

Simplify. $$ 4^{0}-4^{1} $$

Short Answer

Step by step solution

Understanding Exponent Rules

Simplify Each Term

Simplify the Second Term

Subtract the Terms

Key Concepts

Simplifying Expressions

Zero Exponent Rule

Subtraction of Terms

One App. One Place for Learning.

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