Problem 20 - Algebra 1: Concepts and Skills

Question

Evaluate the power. \(9^{2}\)

Step-by-Step Solution

Answer

The value of \(9^{2}\) is 81.

Step 1: Understand the notation

The notation \(9^{2}\) means that we are multiplying 9 by itself. This is because the power (which is the small number 2) indicates how many times we should multiply the base (which is the large number 9).

Step 2: Perform the operation

To find the value of \(9^{2}\), you have to multiply 9 by itself, this will give: \(9 \times 9 = 81\).

Key Concepts

Power Notation

Power notation is a way to express repeated multiplication of the same number. It involves two main parts: the base and the exponent. When you see an expression like \(9^{2}\), it's known as a power. The numeral at the top, called the exponent (2, in this case), tells you how many times you should multiply the base, the larger number below it, which is 9.
Power notation simplifies the way we write and read expressions involving multiplication of the same number.

• "\(9^{2}\)" tells us to multiply the base (9) by itself, resulting in the expression \(9 \times 9\).
• Instead of saying "9 multiplied by itself 2 times," power notation provides a concise form.

Understanding power notation is key to solving many mathematical problems efficiently.

Multiplication

When dealing with exponents, the primary mathematical operation involved is multiplication. Exponents are essentially a shorthand for saying "multiply this number by itself a certain number of times."
For \(9^{2}\), you follow these steps:

• Identify the base (9) and the exponent (2).
• Use multiplication to repeat the base number 2 times because the exponent is 2.
• The result of \(9 \times 9\) is 81, which means \(9^2 = 81\).

Multiplication is crucial here because it enables us to quickly arrive at the result of the power. Always remember:

• The exponent tells you how many times to use multiplication.
• Practicing with different bases and exponents can make you more comfortable with this operation.

Base and Exponent

The terms base and exponent are fundamental when working with powers.
- **Base**: The number that is being multiplied. In the expression \(9^{2}\), the number 9 is the base.- **Exponent**: Indicates how many times the base is used as a factor. In \(9^{2}\), 2 is the exponent.These terms help us break down the expression into more understandable parts.

• The base determines the size of the numbers you'll work with.
• The exponent tells you how many times you'll multiply the base by itself.
• In a real-world context, understanding these elements can help solve complex problems (e.g., calculating area, compound interest).

So, whenever you see a power expression like \(9^{2}\), quickly identify the base and exponent to proceed with the calculations.