Problem 3 - Algebra 1: Concepts and Skills

Question

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

Step-by-Step Solution

Answer

125

Step 1: Understand the problem

We have an expression of the form \(a^{m}/a^{n}\), where \(a\) is the common base and \(m\) and \(n\) are the exponents. The expression can be simplified using the quotient of powers property, which states that \(a^{m}/a^{n}=a^{m-n}\). In our case, \(a=5\), \(m=4\) and \(n=1\).

Step 2: Applying the quotient of powers property

Applying this property to our problem, we subtract the exponent in the denominator (1) from the exponent in the numerator (4). This gives us \(5^{4-1}\) or \(5^{3}\).

Step 3: Solving the power

Our final solution is to perform the power operation. For \(5^{3}\), we multiply 5 by itself two more times, which gives us a solution of 125.