/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 63 Simplify each expression. $$ ... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 63

Simplify each expression. $$ 7^{0} $$

Short Answer

Expert verified
7鈦� simplifies to 1.

Step by step solution

01

Understand the Zero Exponent Rule

According to the zero exponent rule, any nonzero number raised to the power of zero is equal to one. This is a fundamental rule in exponents and applies to our expression 7鈦�.
02

Apply the Zero Exponent Rule

Apply the zero exponent rule to the expression 7鈦�. Since 7 is a nonzero number, 7 raised to the power of zero is: \[ 7^0 = 1 \]

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Key Concepts

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

Understanding Exponents
Exponents are a way to express repeated multiplication of a number by itself. The base number is the number being multiplied, and the exponent tells us how many times the base number is used as a factor in the multiplication. For example, in the expression \(3^4\), 3 is the base and 4 is the exponent. This means that 3 is multiplied by itself four times, or \(3 \times 3 \times 3 \times 3 = 81\).

Exponents are a powerful tool in mathematics because they allow us to write large numbers or repeated operations in a compact form. They are used in many areas such as algebra, calculus, and beyond, making them a crucial concept to understand.
Simplifying Expressions
Simplifying mathematical expressions involves reducing them to their simplest form, making them easier to understand or compute. When dealing with expressions involving exponents, simplification might include applying various exponent rules, such as the zero exponent rule.

To simplify an expression like \(7^0\), we apply the zero exponent rule, which states that any nonzero base raised to the power of zero equals one. Thus, \(7^0\) simplifies to 1. This practice helps eliminate complexity in expressions and focuses on their essential elements, a key skill in mathematics.
Mathematical Rules in Simplification
Mathematical rules, such as the zero exponent rule, play a significant role in simplifying expressions. The zero exponent rule is simple but mighty, as it applies broadly: if you have a base of any nonzero number, and it's raised to an exponent of zero, the result is always one. This not only simplifies the specific case of exponents but also exemplifies the broader structure and consistency found in mathematics.

Rules like these help us navigate complex expressions effortlessly and are foundational in algebra and beyond. Remember :
  • Zero exponent rule: \(a^0 = 1\), for any nonzero \(a\).
  • Understanding these rules will provide you with the tools to simplify more intricate mathematical expressions.

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Most popular questions from this chapter

It was stated earlier that for an integer \(n\) \(x^{-n}=\frac{1}{x^{n}}, \quad x \neq 0\) Explain why \(x\) may not equal 0 .

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