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Chapter 10: Problem 23

Simplify. $$6 x^{0}$$

Short Answer

Expert verified
6

Step by step solution

01

Understand the Exponent Rule

Recall the exponent rule that any non-zero number raised to the power of zero is equal to 1. Mathematically, this is written as follows: \[a^{0} = 1 \text{ for any } a eq 0\]
02

Apply the Rule to the Given Expression

Apply the exponent rule to the given expression \(6x^{0}\). According to the rule, \(x^{0}\) equals 1.
03

Simplify the Expression

Substitute 1 for \(x^{0}\) in the given expression: \[6x^{0} = 6 \cdot 1 = 6\]

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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 crucial skill in algebra. It involves reducing an expression to its simplest form. This makes it easier to work with and understand. To simplify an expression, you often use various algebraic rules and properties. For example, you can combine like terms, use the distributive property, or apply exponent rules. Consider the expression from the exercise: \(6x^{0}\). By recognizing and applying the zero exponent rule, we simplified this expression to \(6\). Understanding how to simplify expressions can help solve equations and understand more advanced mathematical concepts.
Basic Algebra
Basic algebra is the foundation of math that deals with variables, expressions, and equations. It allows us to express relationships and solve for unknowns. Key elements of basic algebra include operations with variables, understanding coefficients, and using algebraic properties. In the context of the given exercise, basic algebra skills help recognize the use of exponents and apply the appropriate rules. For instance, identifying that \(x^{0}\) simplifies to 1 due to the zero exponent rule is a fundamental aspect of basic algebra. Mastering these basic concepts allows for progression to more complex problems and topics.
Zero Exponent Rule
The zero exponent rule is a fundamental principle in algebra. It states that any non-zero number raised to the power of zero equals 1. This can be written mathematically as follows: \[a^{0} = 1 \text{ for any } a eq 0\]. This rule simplifies expressions with exponents. In our exercise, \(x^{0}\) equals 1, simplifying \(6x^{0}\) to \(6 \times 1 = 6\). Understanding the zero exponent rule is important for simplifying and solving algebraic expressions. It helps with reducing complexity and solving equations involving variables with zero exponents.

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Most popular questions from this chapter

Subtract the polynomials. $$\left(12 c^{2}+6 c-3\right)-\left(4 c^{2}-3 c+8\right)$$

Write the opposite of the polynomial. $$2.4 m-5.1 n$$

Fill in the missing polynomial. $$(\quad)(z-5)=z^{2}-3 z-10$$

Find the missing polynomial. \((9 y-3)+(\quad)=-4 y+7\).

Simplify the expression. $$\left(x^{2}\right)^{10}$$
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