Question

Use the quotient of powers property to simplify the expression. $$ \frac{5^{4}}{5^{1}} $$

Short answer

The simplified expression is 125.

Step-by-step solution

Identify the Quotient of Powers Property

The quotient of powers property states that for any non-zero numbers and integers m and n, \(a^{m}/a^{n} = a^{m-n}\). This rule can be applied here because both terms in the expression have the same base, which is the number 5.

Apply the Quotient of Powers Property

Apply the quotient of powers property to simplify the expression. Consequently, the expression \(5^{4}/5^{1}\) becomes \(5^{4 - 1}\), because 4 is subtracted by 1, which is the operation indicated by the quotient of powers property.

Simplify the Resulting Expression

Simplify the resulting expression, \(5^{4 - 1}\) becomes \(5^{3}\).

Calculate the final Answer

Calculate the final answer, \(5^{3}\) results into 125.