Problem 85 - Prealgebra

Question

Multiply. $$2^{2} \cdot 3 \cdot 5$$

Step-by-Step Solution

Answer

The result of the multiplication is 60.

Step 1: Calculate the power

First, calculate the power of 2 in the term \(2^2\). Since any number to the power of 2 means the number is multiplied by itself, we have:\(2^2 = 2 \times 2 = 4\).

Step 2: Multiply by 3

Now that you've found that \(2^2 = 4\), multiply this by 3. This step can be broken down as follows:\(4 \times 3 = 12\).

Step 3: Multiply by 5

Take the result from step 2 and multiply it by 5:\(12 \times 5 = 60\).

Key Concepts

Understanding Multiplication

Multiplication is like adding a number to itself a certain number of times. It's a basic arithmetic operation that helps simplify repeated addition. If you see something like "2 multiplied by 3," it means you have two groups of three.
For example, when you need to multiply numbers like in the problem \(2^2 \cdot 3 \cdot 5\), you're combining all the numbers into one larger product. Each step multiplies the result of the previous multiplication, making the process faster than adding numbers repeatedly.

• Numbers are multiplied in steps, where you take two numbers and get a product.
• It's a foundational math skill used in daily life, like when calculating prices or distances.
• Mastering multiplication helps in understanding more complex math concepts, such as division and fractions.

Exploring a Step-by-Step Solution

When solving a math problem, breaking it down into smaller, manageable parts makes it easier.
Take for instance our exercise \(2^2 \cdot 3 \cdot 5\). Approaching it step-by-step helps clarify the solution.
First, compute \(2^2\). This means multiplying the number 2 by itself, resulting in 4. Next, use this result to continue the process with the next number. Multiply this 4 by 3 to get 12. Finally, multiply 12 by 5 to reach the final product of 60.

• This approach prevents mistakes by focusing on one operation at a time.
• Step-by-step solving builds confidence and improves understanding.
• It's helpful for homework, exams, and real-life problem-solving.

Grasping the Powers of Numbers

The concept of powers, such as in \(2^2\), is a way to express repeated multiplication of the same number. Exponents indicate how many times to multiply a base number by itself. In mathematics, this makes calculations more efficient.
For instance, \(2^2\) means \(2 \times 2\). Here, 2 is the base, and the exponent 2 signifies two instances of multiplication. This is especially useful when dealing with large bases or higher powers.

• Exponents simplify notation, making complex calculations manageable.
• Understanding powers is crucial for advanced topics, like algebra and calculus.
• Recognizing and working with powers aids in financial calculations, scientific computations, and more.