Question

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

Short answer

The simplified expression is \(1/m^{6}\).

Step-by-step solution

Identify the Base and Exponents

The base in both the numerator and the denominator is 'm'. The exponent in the numerator is 5 and the exponent in the denominator is 11.

Apply the Quotient of Powers Property

The quotient of powers property states that \(a^{m}/a^{n} = a^{m-n}\). Thus, we subtract the exponent in the denominator from the exponent in the numerator: \(5 - 11 = -6\). The expression can now be rewritten as \(m^{-6}\).

Simplifying Negative Exponent

Negative exponents can be simplified by placing the base with its exponent in the denominator of a fraction. This will create a positive exponent. So, the final simplified expression is \(1/m^{6}\).