Problem 11 - Fundamentals of Mathematics

Question

Determine the value of each power and root. \(15^{2}\)

Step-by-Step Solution

Answer

The value of \(15^2\) is 225.

Step 1: Understanding Exponents

The expression \(15^{2}\) means we need to multiply 15 by itself. The base number here is 15, and the exponent is 2, indicating how many times the base number is used in the multiplication.

Step 2: Calculating the Power

To solve \(15^{2}\), multiply 15 by 15. This can be computed as follows: \[15 \times 15 = 225\]

Step 3: Verify the Calculation

Double-check the calculation to ensure its correctness. Multiplying again confirms that \(15 \times 15 = 225\), which verifies that our previous calculation was accurate.

Key Concepts

Power Calculation

When we talk about power calculation in mathematics, we are referring to the operation involving exponents. This process allows us to express repeated multiplication in a simpler form using two key components: the base number and the exponent.
In the given exercise, we need to calculate the power of 15 raised to 2, written as \(15^2\). This expression means that we multiply the base number, 15, by itself as many times as indicated by the exponent, which is 2 in this case.
Power calculations are used to simplify many mathematical expressions, enabling us to handle large numbers or repeated multiplications more efficiently. By applying this operation, we arrive at 225, which is the result of \(15 imes 15\).

Base Number

The base number is a fundamental part of any power expression. It is the number that we multiply by itself according to the number of times specified by the exponent. In our example, the base number is 15, and it plays a crucial role in determining the final product.
Whenever you see an expression like \(b^n\), you know "b" is the base number that you'll be working with. Understanding the base is essential because it directly influences the calculation's outcome.
Whenever you face a power calculation, identifying this component helps you set the groundwork for finding the result as you proceed with the multiplication steps.

Mathematics Operations

Mathematics operations are the building blocks for solving problems in math, and they often involve exponents just like in this exercise. Each operation follows specific rules and allows us to manipulate numbers to obtain desired results.
Here, we are primarily discussing the multiplication involved in power calculations. Multiplication is a basic operation that combines groups of numbers. When combined with exponents, it transforms into repeated multiplication, like \(15^2 = 15 \times 15\).
Exponents themselves are a type of mathematical operation that leads to power calculations. They help to condense long multiplication processes, providing a shorthand way of indicating the number of times a base number is used as a factor. This efficient notation not only simplifies calculations but also aids in identifying patterns and relationships in numbers.