Problem 4 - Elementary and Intermediate Algebra

Question

Write exponential notation. $$ y \cdot y \cdot y \cdot y \cdot y \cdot y $$

Step-by-Step Solution

Answer

y^6

Step 1: Identify the Base

Determine the number being multiplied repeatedly. Here, the repeated factor is 'y'.

Step 2: Count the Number of Factors

Count how many times 'y' is multiplied. There are six 'y' terms.

Step 3: Write in Exponential Notation

Express the repeated multiplication using exponents. This can be written as \(y^6\).

Key Concepts

base number

The base number is a key part of understanding exponential notation. When you see an exponential expression like \(y^6\), the 'base number' is the number that is being multiplied by itself. In our example, the base number is 'y'. This means 'y' is the number repeatedly multiplied.
Simple examples help clarify this concept:

• In the expression \(3^4\), '3' is the base number.
• In \(a^5\), the base is 'a'.

Understanding the base number is vital because it's the fundamental building block of exponential notation and repeated multiplication.

exponential expression

An exponential expression is a shorthand way to represent repeated multiplication of a base number. Instead of writing a number multiple times, you use exponents. An exponential expression has two parts:

• The base number: the number being multiplied.
• The exponent: the number of times the base is multiplied by itself.

Consider the expression \(y^6\):

• 'y' is the base number.
• '6' is the exponent, telling us that 'y' is multiplied six times.

This saves time and space, making complex problems easier to work with!

repeated multiplication

Repeated multiplication is what exponential expressions stand for.
It's the process of multiplying the same number over and over. Instead of writing 'y' six times like \(y \cdot y \cdot y \cdot y \cdot y \cdot y\),
we use exponential notation \(y^6\) for simplicity. This approach makes calculations and expressions clearer. Some benefits of using exponential notation for repeated multiplication include:

• Easier to read and understand.
• Reduces the complexity in both writing and calculating.
• Helps in solving higher-level math problems more efficiently.

So, whenever you see repeated multiplication of the same number, think of how you can simplify it using exponential notation.