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Multiplication and Division with Exponents Using Integral Bases

Multiplication and division with exponents using integral bases is a common math topic that is taught to students in Grade 9 in Ontario, Canada. It is a skill that can be difficult for students with Dyslexia to understand, but with guidance and practice, they can become comfortable with the concept.

Put simply, multiplication and division with exponents using integral bases is a way of expressing multiplication and division that uses numbers that are raised to a power, also known as an exponent. This can look like this equation:

A Sample Equation: x^2 * x^3 = x^5

In this example, the individual numbers (x and 2) are known as the bases, which are multiplied to create the result x^5.

As mentioned, multiplication and division with exponents using integral bases can be difficult for students with Dyslexia. Here are 3 examples of issues that may arise, and how you can help the 14 year old better understand the concept:

Issue 1: Confusing the Operator and Base

Students with Dyslexia can often have difficulty differentiating between the operator (the sign that tells the equation what operation is taking place) and the base (the individual number in the equation). Help the 14 year old better understand these key concepts by emphasizing to them the differences between an operator and base and how they each have a distinct purpose. When solving the equation, guide your student by emphasizing that they need to focus on the imaginary line that separates the left side from the right side.

Issue 2: Confusing Exponents With Powers

The concept of a power or exponent can be challenging for many students with Dyslexia. To help your student better understand this concept, explain to them that exponents are like multiplication, but the number being multiplied is on the opposite side of the operator. Showing an example of the equation on paper and having your student write it out can help to give them a better understanding of this concept.

Issue 3: Multiplying and Dividing Exponents with Different Bases

Multiplying and dividing exponents with different bases can be a potentially confusing concept for students with Dyslexia. To help your student wrap their head around this, provide an example of what the equation might look like on paper, and discuss with them how no matter what the numbers are on each side of the operator, the result will always be a single number. Make sure to emphasize that when the equation has the same base, the answer is always the sum of the two exponents; but when the equations have different bases, the result will always be one number.

To help your student better understand multiplication and division with exponents using integral bases, provide examples of what the equation might look like on paper. Discuss and explain the differences between the operator and base, and the concept of a power or exponent. Provide an example of what the equation might look like when multiplying and dividing different bases, and emphasize that the results will always be a single number.

Reference: x^2 * x^3 = x^5

Sample Question: What is the answer when 4^2 is multiplied by 4^5?

Answer: 4^7

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