Question

1. simplify (hint: quotient rule of exponents) \\(\frac{n^{100}}{n^{10}}\\)

Explanation:

Step1: Recall quotient rule of exponents

The quotient rule of exponents states that for any non - zero base \(a\) and integers \(m\) and \(n\), \(\frac{a^{m}}{a^{n}}=a^{m - n}\). Here, the base \(a = n\), \(m = 100\) and \(n = 10\).

Step2: Apply the quotient rule

Using the quotient rule \(\frac{n^{100}}{n^{10}}=n^{100 - 10}\)

Step3: Simplify the exponent

Calculate \(100-10 = 90\), so \(\frac{n^{100}}{n^{10}}=n^{90}\)

Answer:

\(n^{90}\)