Problem 10 - Algebra 1

Question

Use the power of a power property to simplify the expression. $$ (3)^{2} $$

Step-by-Step Solution

Answer

The simplified form of the expression \( (3)^{2} \) is 9.

Step 1: Apply the exponent

\((3)^2 = 3 \times 3 = 9\)

Step 2: State the result

The simplified form of \((3)^2\) is \(\boxed{9}\).

Key Concepts

Power of a Power Property

In mathematics, the power of a power property is a key concept when dealing with exponents. It helps simplify expressions that involve raising a power to another power. When an expression is in the form \[ (a^m)^n \]this property tells us that we can multiply the exponents together: \[ a^{m \cdot n} \]This means instead of doing multiple steps or calculations to reach the result, we can apply this rule and directly reduce the complexity. Understanding and applying the power of a power property can make working with exponents more efficient and less time-consuming. Start by identifying expressions that can use this property and practice applying it across various problems. Recognizing when to use this property will come with practice and will help in managing more complex exponent-related expressions.

Simplifying Expressions

Simplifying expressions is all about making them easier to work with and understand. One primary goal when simplifying is to perform operations within the expression until it's reduced to its simplest form. For instance, when given an expression like \((3)^2\),we're aiming for a single number, if possible.

• Begin by identifying operations that can be performed immediately.
• Follow the rules of arithmetic and the specific properties of exponents.
• In our example, \( (3)^2 \) simplifies because you're multiplying 3 by itself once, which equals 9.

Simplifying correctly ensures that the expressions are clear and accurate. Additionally, practicing this skill will support solving more complicated mathematical problems in the future. Look for patterns and rules, like those involving exponents, and apply them to break down the expression seamlessly.

Squared Numbers

Squared numbers are a special type of exponent where a number is multiplied by itself. This is usually expressed as \(a^2\).Understanding squared numbers is fundamental because they're frequently used in various math problems, calculations, and formulas. For instance, when you see \(3^2\),this simply means \(3 \times 3\),which gives the result of 9. Here are some key points:

• Squaring makes numbers grow quickly; understanding that a seemingly small base number can become significantly larger.
• It's also the basis for understanding higher-level math concepts like quadratics and areas in geometry.
• Recognizing that written expressions like \( (3)^2 \) can be simplified can save time and reduce mistakes.

Mastering squared numbers builds confidence in handling more complex exponentials and other related mathematical concepts.