Question

use the quotient rule and simplify the expression.\\(\frac{(-3)^6}{(-3)^4}\\)\\(\frac{(-3)^6}{(-3)^4} = square\\)

Explanation:

Step1: Recall the quotient rule for exponents

The quotient rule for exponents states that for any non - zero number \(a\) and integers \(m\) and \(n\), \(\frac{a^{m}}{a^{n}}=a^{m - n}\). Here, \(a=- 3\), \(m = 6\) and \(n=4\).
So, \(\frac{(-3)^{6}}{(-3)^{4}}=(-3)^{6 - 4}\)

Step2: Simplify the exponent

Calculate \(6-4 = 2\). So we have \((-3)^{2}\)

Step3: Evaluate \((-3)^{2}\)

By the definition of exponentiation, \((-3)^{2}=(-3)\times(-3)=9\)

Answer:

\(9\)