What is the Quotient Rule of Integer Exponents
The quotient rule of integer exponents states that when dividing two numbers with the same base but different exponents, you can subtract the exponents. Mathematically, if a is any non-zero real number and m and n are integers, then:
a^m / a^n = a^(m - n)
For example, if you have 2^6 / 2^3, you can apply the quotient rule to get:
2^6 / 2^3 = 2^(6 - 3) = 2^3 = 8
The Quotient Rule of Integer Exponents states that when dividing two numbers with the same base, you should subtract the exponents. In mathematical notation, it can be written as:
a^m / a^n = a^(m - n)
where "a" is the base and "m" and "n" are the exponents.
The Quotient Rule of Integer Exponents is a rule used to simplify expressions involving exponents. It states that when dividing two numbers with the same base but different exponents, the exponents can be subtracted from each other.
Here's the mathematical expression of the Quotient Rule of Integer Exponents:
a^m / a^n = a^(m-n)
To understand how to use the Quotient Rule, let's break it down into steps:
Step 1: Identify the base. The base is the number that is raised to the exponent. In this case, we have "a" as the base.
Step 2: Determine the exponents. The exponents are the powers to which the base is raised. In this case, we have "m" and "n" as the exponents.
Step 3: Subtract the exponents. After identifying the base and exponents, subtract the smaller exponent from the larger exponent. This subtraction step simplifies the expression.
Step 4: Rewrite the expression. Finally, rewrite the expression using the base and the result from the subtraction as the new exponent.
For example, let's say we have the expression 7^4 / 7^2. Using the Quotient Rule of Integer Exponents, we can simplify it as follows:
Step 1: The base is "7".
Step 2: The exponents are "4" and "2".
Step 3: Subtract the exponents: 4 - 2 = 2.
Step 4: Rewrite the expression: 7^4 / 7^2 = 7^(4-2) = 7^2 = 49.
Therefore, the simplified expression is 49.