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Chapter 2: Problem 5

Evaluate. $$6^{0}$$

Short Answer

Expert verified
The expression \(6^{0}\) can be evaluated using the rule of exponents \(a^0 = 1\). Applying this rule, we find that \(6^0 = 1\).

Step by step solution

01

Remember the Rule of Exponents

According to the rule of exponents, any non-zero number raised to the power of 0 is equal to 1, i.e. \(a^0 = 1\).
02

Apply the Rule to the Given Expression

Now, we have to evaluate \(6^0\). Using the rule \(a^0 = 1\), we can say that \(6^0 = 1\).
03

Write the Final Answer

After applying the rule of exponents, we find that the evaluation of \(6^0\) results in the number 1. Therefore, \(6^0 = 1\).

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Key Concepts

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

Zero Exponent Rule
Understanding the zero exponent rule is crucial in algebra. This rule states that any non-zero number raised to the power of zero is equal to 1. This might seem a bit counterintuitive at first, but let's unravel this. If you have, say, 5, then multiplying it by itself zero times might seem like it becomes zero. But in mathematics, repeating an operation zero times isn't the same as it not existing鈥攊t defaults to a baseline of one.
  • Any number except zero raised to 0 equals 1. This is a fundamental rule in exponential functions.
  • Keep in mind: Zero itself (0) raised to zero, however, is indeterminate. It鈥檚 a special case where math gets complex.

This rule helps simplify expressions and solve equations, making it an essential part of your algebra toolkit.
Evaluating Expressions
Evaluating expressions involves calculating the value of a mathematical phrase. When expressions include exponents, you must apply exponent rules carefully. Let鈥檚 take an example expression: 6 raised to the power of 0, or \(6^0\). Here's how you break it down:
  • Identify parts of the expression: base (6) and exponent (0).
  • Apply the zero exponent rule which tells us \(b^0 = 1\) for any base \(b\) not equal to zero.
  • Write out the result: since \(6^0 = 1\).

By applying known rules of exponents, the process becomes systematic. So, evaluating expressions with exponents involves a mix of understanding the rules and practicing them.
Algebra Basics
Algebra sets the foundation for understanding mathematical relations and operations like addition, subtraction, multiplication, division, and exponentiation. When working with algebra:
  • Variables and constants are building blocks used to express these operations.
  • Expressions represent sums, products, and powers, often written with variables.
  • Simplification is key: using rules and operations to make expressions manageable.

In the context of exponents, algebraic basics apply rules such as the zero exponent rule to explore patterns and problem-solve more efficiently. Knowing these basics makes more complex algebra possible, laying groundwork for further mathematical study.

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Most popular questions from this chapter

Simplify the expression using the product rule. Leave your answer in exponential form. $$10 c^{8} \cdot c^{2} \cdot c$$

Simplify the expression using the product rule. Leave your answer in exponential form. $$a^{2} \cdot a^{3}$$

Perform the operation as indicated. Write the final answer without an exponent. \(\left(2.3 \times 10^{3}\right)\left(3 \times 10^{2}\right)\)

Perform the operation as indicated. Write the final answer without an exponent. \(\left(3.19 \times 10^{-5}\right)+\left(9.2 \times 10^{-5}\right)\)

Write each number in scientific notation. 990
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