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Chapter 10: Problem 641

Simplify each expression. $$\left(47 a^{18} b^{23} c^{5}\right)^{0}$$

Short Answer

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Step by step solution

01

Understanding the Zero Exponent Rule

Any non-zero number raised to the power of zero is equal to 1. This is known as the zero exponent rule. Formally, for any non-zero number or variable ({x}), ({x^0 = 1}).
02

Applying the Zero Exponent Rule

In the given expression, ((47 a^{18} b^{23} c^{5})^0), everything inside the parentheses is raised to the power of zero. According to the zero exponent rule, this simplifies to 1.

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Key Concepts

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

Exponent Rules
Exponent rules are essential in simplifying expressions in algebra. One key rule is the zero exponent rule. This rule states that any non-zero number raised to the power of zero is equal to 1. For example, if we have a variable \(x\), then \(x^0 = 1\). This rule makes it easy to simplify expressions, as it reduces everything to 1 when we see an exponent of zero.
Simplifying Expressions
Simplifying expressions is an important skill in algebra. It allows us to break down complex equations into more manageable parts. When applying exponent rules like the zero exponent rule, we can significantly simplify our work. For instance, consider the expression \( (47 a^{18} b^{23} c^{5})^0 \). By applying the zero exponent rule, we know that anything raised to the power of zero equals 1. Therefore, \( (47 a^{18} b^{23} c^{5})^0 \) simplifies directly to 1. Simplifying expressions helps in solving algebraic problems more efficiently.
Basic Algebra Concepts
Understanding basic algebra concepts is foundational for advancing in mathematics. One such concept is how to handle exponents. Let's review:
  • Exponents tell us how many times to multiply a number by itself.
  • For example, \(a^2\) means \(a \times a\).
  • Knowing the rules of exponents, such as the zero exponent rule, can simplify many problems.

In our example, \( (47 a^{18} b^{23} c^{5})^0 \), everything inside the parentheses is raised to zero, demonstrating our understanding of exponents. Using the zero exponent rule, we simplify this to 1 without much calculation. Mastering these basic concepts will make future algebra problems easier to tackle.

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Most popular questions from this chapter

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