Problem 67 - Algebra 1

Question

Write the expression in exponential form. four squared

Step-by-Step Solution

Answer

\(4^2\)

Step 1: Identify the base

In the expression 'four squared', 'four' is the base of the exponent. The base is the number that is being raised to a power.

Step 2: Identify the exponent

In the expression 'four squared', 'squared' indicates that the base is raised to the power of 2. Thus, the exponent here is 2.

Step 3: Write in exponential form

In exponential form, the base is followed by the exponent to the upper right. Following steps 1 and 2, in this exercise, 'four squared' can be written as \(4^2\).

Key Concepts

Base

The base in any exponential expression is the number or variable that is being multiplied by itself a certain number of times. In 'four squared', the base is 'four'. Understanding the base is crucial because it tells us what number is involved in the repeated multiplication. Let's break it down a bit:

• Consider the expression \[ 4^2 \] Here, '4' is the base.
• It implies that the number 4 is used as a factor twice when multiplied together.
• Thus, while addressing the base, always ask: "What is being multiplied repeatedly?"

This simple identification will help you translate word problems and numerical expressions into exponential form with ease.

Power

In mathematics, a power refers to the exponent in an exponential expression. It tells us how many times the base is multiplied by itself. When we read 'four squared', 'squared' means to multiply the base two times. Here's how it applies:

• The power indicates 'how many times?' So if it's 2, just like in \[4^2\], the number 4 is used as a factor two times: 4 × 4.
• The power is crucial for determining the value of the exponential expression.

Therefore, understanding the power allows us to determine the scale or extent of the multiplication happening within the expression.

Exponential Form

The exponential form is a mathematical shorthand to represent repeated multiplication of a base number. When given the phrase 'four squared', it can be written concisely in exponential form as \(4^2\). Here’s why this form is preferred:

• It saves space and provides clarity, especially with larger numbers or factors.
• It's a universal representation, easily understood across various mathematical concepts and fields.

Additionally, using exponential form helps in performing operations such as differentiation and integration in calculus. So when you translate an expression into exponential form, you're not just rewriting it – you're making it functional for further mathematical manipulation.