Problem 96 - Algebra 1

Question

Write the expression in exponential form. seven squared

Step-by-Step Solution

Answer

The expression 'seven squared' in exponential form is \(7^2\).

Step 1: Understand the Expression

The term 'seven squared' means that the number 7 is multiplied by itself. This is gained from understanding that 'squared' in mathematical terms refers to raising a number to the power of 2.

Step 2: Write in Exponential Form

Knowing what 'squared' stands for, the expression can now be rewritten in exponential form. So, 'seven squared' translates to \(7^2\).

Key Concepts

Exponential Form

When we talk about exponential form, we're referring to a way of expressing repeated multiplication of a number by itself. In simple terms, if a number is multiplied by itself a certain number of times, this repeated multiplication can be conveniently written using an exponent. This notation helps simplify expressions and make it easier to work with large numbers. For example, in the expression \(7^2\), the number 7 is called the base, and 2 is the exponent. The entire expression is read as "seven to the power of two," which means multiplying 7 by itself one time, resulting in 49.

• Base: The number that is multiplied.
• Exponent: Indicates how many times the base is used in multiplication.

Understanding exponential form is key to grasping other mathematical concepts like scientific notation and polynomial expressions. It's a building block that simplifies complex multiplication.

Squared

The term 'squared' is a specific use of exponents where the exponent is 2. Squaring a number simply means multiplying the number by itself. This concept is common when dealing with areas of squares in geometry, hence the name 'squared.'
When we say a number is 'squared,' such as in the expression 'seven squared,' it indicates the use of the exponent 2 on the base number. Therefore, 'seven squared' is written as \(7^2\), equal to 49. It's important to remember:

• 'Squared' always means using an exponent of 2.
• It is a quick way to calculate the area of a square with sides of equal length.

Squaring is used in different math fields, including algebra and geometry, to solve diverse problems efficiently.

Powers

Powers express how many times to use a number in a multiplication, where the number being multiplied is called the base, and the power is the number of times it is used as a factor. This expression, known as 'raising to the power,' allows us to express large computations succinctly.
Every power expression has two parts:

• The base: The number used in multiplication.
• The power (or exponent): How many times the base occurs in the multiplication.

For instance, in \(7^2\), 7 is the base and 2 is the power, indicating that 7 is used twice in multiplication to give us 49. Understanding powers is essential for tackling exponential growth problems, calculating compound interest, and working with polynomial expressions in algebra. Properly grasping powers will pave the way for solving more complex technical problems in mathematics.