Problem 27 Simplify. $$\left(\frac{1}{3}\... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 10: Problem 27

Simplify. $$\left(\frac{1}{3}\right)^{0}$$

Short Answer

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Step by step solution

- Understand 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.

- Apply the Zero Exponent Rule

In the given expression, $ \left( \frac{1}{3} \right)^{0} $, the base is a non-zero number. According to the Zero Exponent Rule, $ \left( \frac{1}{3} \right)^{0} = 1 $.

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Key Concepts

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

exponentiation

Exponentiation is a fundamental operation in mathematics. It involves raising a number to a power. In simpler terms, if you have a base number like 3 and an exponent such as 2, you write it as 3虏. This means multiplying the base by itself: 3 脳 3 = 9.

Exponentiation helps in many mathematical areas, such as growth calculations, scientific notation, and complex equations. Understanding how to handle exponents, especially special cases like zero, is crucial.

Remember that the base can be any number, positive, negative, or even a fraction. The exponent tells you how many times to multiply the base by itself.

simplifying expressions

Simplifying expressions means making them easier to work with. You use various rules and operations to reduce complexity. The zero exponent rule is one of these tools.

When simplifying, always look for obvious simplifications first. For instance, any term to the power of zero simplifies directly to 1. Like in the given problem, $ \left( \frac{1}{3} \right)^{0} = 1 $.

Other rules help too, such as combining like terms, factoring, and using the distributive property. Knowing these makes solving equations faster and clearer.

prealgebra concepts

Prealgebra lays the groundwork for all future math learning. It includes basics like operations, variables, and simple equations. Exponents fall into this category.

The zero exponent rule is a foundational concept introduced in prealgebra. It states that any non-zero number raised to the power of zero equals 1. This rule simplifies equations and helps solve problems efficiently.

Understanding prealgebra deeply ensures success in higher-level math. Concepts like exponentiation and simplification build on each other, forming a strong mathematical foundation.

Practicing these concepts helps solidify your knowledge and makes complex problems seem less daunting.

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91影视

Simplify. $$\left(\frac{1}{3}\right)^{0}$$

Short Answer

Step by step solution

- Understand the Zero Exponent Rule

- Apply the Zero Exponent Rule

Key Concepts

exponentiation

simplifying expressions

prealgebra concepts

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