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Chapter 1: Problem 10

Evaluate. $$ 9^{2} $$

Short Answer

Expert verified
The value of \(9^2\) is 81.

Step by step solution

01

Understand the Problem

The problem requires us to evaluate the expression \(9^2\). This means we need to find the result of raising the number 9 to the power of 2.
02

Apply the Exponent Rule

When a number is raised to the power of 2, it is multiplied by itself. Thus, \(9^2\) can be calculated as \(9 \times 9\).
03

Multiply the Numbers

Perform the multiplication: \(9 \times 9 = 81\).
04

Verify the Result

Double-check the multiplication to ensure accuracy: \(9 \times 9\) is \(81\). Hence, the value of \(9^2\) is correct.

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Key Concepts

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

Squared Numbers
Squared numbers are a special form of number processing where a number is multiplied by itself. This process is also known as raising a number to the power of 2. Squaring a number is a fundamental skill in mathematics and helps in various real-life applications like calculating areas.For example, when you square the number 9, you compute it as:
  • 9 multiplied by 9
  • The operation: \(9 \times 9\)
  • Resulting in: 81
Every squared number has the positive number zero as its exponent, making it a simple yet very important concept to grasp. When learning about squared numbers, always remember that you're simply forming a perfect square with this process.
Multiplication
Multiplication is a basic mathematical operation where a number is added to itself a specified number of times. It is one of the four fundamental arithmetic operations and plays a critical role when working with exponents.When you multiply 9 by 9, consider:
  • The multiplication is repetitive addition. You're adding 9, nine times.
  • This can look like: \(9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9\), which gives us \(81\).
    • The process of multiplication becomes handy when understanding exponents, as an exponent indicates how many times a number will multiply itself. Mastering multiplication is crucial because it simplifies complex calculations, such as those involving exponents or even algebraic equations.
Power of a Number
The power of a number refers to how many times the base number is utilized in the multiplication process. It is represented as an exponent, which appears as a small number raised to the upper right of the base number. In the expression \(9^2\),
  • 9 is the base number.
  • 2 is the exponent, which indicates that 9 will be multiplied by itself once (since it's 9 squared).The power tells you how to scale numbers efficiently. It's a valuable tool for simplifying expressions and managing larger numbers. The power of the number simplifies complicated multiplication processes and turns them into more manageable expressions, which is essential for advanced mathematical problem-solving.

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