Question: Simplify \(\frac{(-5)^{20}}{(-5)^{5}}\), and write as a single power. - \((-5)^{4}\) -…

Simplify \(\frac{(-5)^{20}}{(-5)^{5}}\), and write as a single power.

• \((-5)^{4}\)
• \((-5)^{15}\)
• \(1^{16}\)
• \(1^{4}\)

Solution

The problem is to simplify \[ \frac{(-5)^{20}}{(-5)^{5}} \] and express it as a single power. To simplify this, we use the rule of exponents: \[ \frac{a^m}{a^n} = a^{m-n} \] Apply this rule to the given expression: \[ \frac{(-5)^{20}}{(-5)^{5}} = (-5)^{20-5} \] Calculate the exponent: \[ (-5)^{15} \] So the simplified expression is \[ (-5)^{15} \] The correct answer is \((-5)^{15}\).