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Chapter 4: Problem 39

\(3 x^{0} \quad(x \neq 0)\)

Short Answer

Expert verified
3

Step by step solution

01

- Identify the exponent

Notice that the exponent of the term is 0. In other words, the term is written as \(x^0\).
02

- Apply the zero exponent rule

According to the zero exponent rule, any non-zero base raised to the power of 0 is equal to 1. So, \(x^0 = 1\) when \(x eq 0\).
03

- Simplify the expression

Substitute \(x^0\) with 1 in the original term. The expression becomes \(3 \times 1\).
04

- Calculate the final value

Multiply 3 by 1 to get the final answer, which is 3.

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Key Concepts

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

Exponents
Exponents play a crucial role in algebra and mathematics, simplifying complex expressions. An exponent represents the number of times a base is multiplied by itself. For example, in the expression \(2^3\), the base is 2, and the exponent is 3, meaning \(2^3\) translates to 2 脳 2 脳 2, which equals 8.
  • Such expressions make calculations easier, especially when dealing with large numbers.
  • The zero exponent rule is a special case in the study of exponents.
Understanding these fundamentals is essential for simplifying algebraic expressions effectively.
Algebra
Algebra is the branch of mathematics that deals with symbols and the rules for manipulating them.These symbols represent numbers and are used to express mathematical relationships.
  • In algebra, exponents are used to simplify and solve expressions. Knowing how to apply rules for exponents is key to working efficiently with algebraic equations.
  • In the exercise, we start with the expression \(3x^0\). Here, '3' is a coefficient, and \(x^0\) involves an exponent, which brings us to applying the zero exponent rule.
Understanding the different rules in algebra, like the zero exponent rule, helps to simplify equations and solve them systematically.
Simplification
Simplification in mathematics involves reducing an expression to its most basic form. This makes expressions easier to understand and solve.
  • In the given exercise, after recognizing the exponent is zero, the zero exponent rule tells us that \(x^0 = 1\).
  • Next, substituting \(x^0\) with 1 in the original expression \(3 \times 1\) simplifies it further.
  • Performing the multiplication, we get the final value of 3.
This simplification process highlights the importance of understanding and applying exponent rules to simplify algebraic expressions effectively.

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Most popular questions from this chapter

Find each product. Recall that \(a^{2}=a \cdot a\) and \(a^{3}=a^{2} \cdot a\). $$ -4 r(3 r+2)(2 r-5) $$

The special product \((x+y)(x-y)=x^{2}-y^{2}\) can be used to perform some multiplications.Example: $$\begin{array}{l|l}51 \times 49 & 102 \times 98 \\\=(50+1)(50-1) & =(100+2)(100-2) \\\=50^{2}-1^{2} & =100^{2}-2^{2} \\\=2500-1 & =10,000-4 \\\=2499 & =9996\end{array}$$ Use this method to calculate each product mentally. $$ 20 \frac{1}{2} \times 19 \frac{1}{2} $$

Find each product. $$ (3 t-4 s)(t+3 s) $$

Graph each equation by completing the table of values. $$\begin{aligned} &y=x^{2}-9\\\&\begin{array}{c|c}\hline x & y \\\\\hline-2 & \\\\\hline-1 & \\\\\hline 0 & \\\\\hline 1 & \\\\\hline 2 &\end{array}\end{aligned}$$ $$

$$ \begin{aligned} &y=-x^{2}+2\\\ &\begin{array}{c|c} \hline x & y \\ \hline-2 & \\ \hline-1 & \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \end{array} \end{aligned} $$
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