Problem 86 - Prealgebra

Question

Expand and multiply. $$4^{2}$$

Step-by-Step Solution

Answer

\(4^2 = 16\)

Step 1: Understanding the expression

The expression given is \(4^2\), which means "4 raised to the power of 2".

Step 2: Interpreting the exponent

The exponent 2 in \(4^2\) indicates that the base 4 needs to be multiplied by itself once. So, \(4^2 = 4 \times 4\).

Step 3: Performing the multiplication

Multiply 4 by itself: \(4 \times 4 = 16\).

Key Concepts

power of a number

When we talk about the "power of a number," we're exploring a concept central to understanding exponents. In mathematics, the power is essentially a shorthand way to express repeated multiplication. For example, when you see something like \(4^2\), this is telling you to multiply the number 4 by itself two times.

• The number 4 is called the "base." It's the number that gets multiplied.
• The number 2, residing at the top, is the "exponent." It tells you how many times to use the base in the multiplication.

This results in the expression \(4^2\) being equal to \(4 \times 4\), which further simplifies to 16.
Grasping the concept of power helps simplify complex calculations, making it an essential tool in math.

multiplication

Multiplication is one of the most fundamental operations in arithmetic. It involves adding a number to itself a certain number of times. For instance, \(4 \times 4\) is a way of expressing "4 added to itself 4 times." When you multiply two numbers, this results in a product.

• In our expression, \(4 \times 4\) is straightforward; it's equivalent to 16.
• Imagine multiplying numbers like cutting a cake into even pieces – each piece representing a multiplication.

By understanding multiplication deeply, you can unlock the ability to navigate through more complex mathematical problems.
Don't forget: multiplication can look different depending on context, but it always involves repeating an addition process.

base and exponent

The terms "base" and "exponent" are crucial for mastering exponential operations.

• The "base" is the main number being multiplied. In our example, the base is 4.
• The "exponent" shows how many times the base is used as a factor, a very dynamic and powerful tool in mathematics. In \(4^2\), the exponent is 2.

Together, the base and exponent form an exponential expression, which offers a concise way to represent repeated multiplication.
Understanding how to break down and compute with bases and exponents opens the door to simplifying and solving various mathematical challenges with ease.