Problem 9 - Algebra 1: Concepts and Skills

Question

Use the quotient of powers property to simplify the expression. $$ \frac{m^{5}}{m^{11}} $$

Step-by-Step Solution

Answer

The simplified form of the expression is \(m^{-6}\).

Step 1: Identify Quotient of Powers Property

Recognize that the exercise calls for using the law of quotient of powers in exponents. This is a rule where the base is the same for each number.

Step 2: Apply Quotient of Powers Property

This rule states that, to divide two exponents with the same base, you subtract the exponent of the divisor \(m^{11}\) from the exponent of the dividend \(m^{5}\). Therefore, you perform the operation \(5 - 11\).

Step 3: Final Solution

The subtraction operation \(5-11\) yields \(-6\), hence we write the simplified form of the given expression as \(m^{-6}\).