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Chapter 1: Problem 18

Simplify. $$ 9^{1} $$

Short Answer

Expert verified
9

Step by step solution

01

Identify the power

Notice that the base of the expression is 9 and the exponent is 1.
02

Apply the exponent rule

When any number is raised to the power of 1, it remains the same. Therefore, apply the rule to simplify the expression.
03

Simplify the expression

Using the exponent rule, simplify the expression: 9^{1} = 9.

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Key Concepts

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

Exponent Rule
To understand the given exercise, let鈥檚 start with the exponent rule. The exponent rule helps us simplify expressions where numbers are raised to a power. One essential rule is the **identity exponent rule**. According to this rule, any number raised to the power of 1 equals itself. In mathematical terms, it鈥檚 written as: \[ a^{1} = a \] So, in the given exercise, 9 raised to the power of 1 remains 9: \[ 9^{1} = 9 \]This makes simplifying exponents straightforward. By applying these rules, we make complex calculations much easier.
Base and Exponent
Before applying the rules, it鈥檚 important to understand the terms **base** and **exponent**. The **base** is the main number that you are multiplying. The **exponent** tells you how many times to multiply the base by itself. In the expression \[ b^{n} \] '**b**' is the base, and '**n**' is the exponent. In the given exercise, \[ 9^{1} \] '**9**' is the base, and '**1**' is the exponent. Since the exponent is 1, you don't actually multiply 9 by itself; you just get 9. Understanding these terms is crucial because they make it easier to apply the exponent rules correctly.
Simplification
Simplifying expressions with exponents makes it easier to understand and solve problems. The simplification process can involve different rules, but in this exercise, we use the identity exponent rule. Here are the steps broken down:
  • Step 1: Identify the base and the exponent. For \[ 9^{1} \] , the base is 9, and the exponent is 1.
  • Step 2: Apply the identity exponent rule: When any number is raised to the power of 1, it remains itself. So, \[ 9^{1} = 9 \]
  • Step 3: Simplify the expression to get the final result: \[ 9^{1} = 9 \]
Simplification like this not only makes expressions easier to handle but also helps in solving larger and more complex problems efficiently. Always break your problem into these steps for easier understanding.

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