Question

simplify. express your answer using positive exponents. \\(\frac{9m^{-4}n^{0}}{9mn^{0}}\\)

Explanation:

Step1: Simplify the coefficient and the constant exponent term

First, we know that any non - zero number to the power of 0 is 1, so \(n^{0}=1\) (assuming \(n
eq0\)). Also, we can simplify the coefficient \(\frac{9}{9} = 1\). The expression becomes \(\frac{1\times m^{- 4}\times1}{1\times m\times1}=\frac{m^{-4}}{m}\)

Step2: Use the quotient rule of exponents

The quotient rule of exponents states that \(\frac{a^{m}}{a^{n}}=a^{m - n}\) (where \(a
eq0\)). For \(a = m\), \(m=-4\) and \(n = 1\), we have \(m^{-4-1}=m^{-5}\)

Step3: Convert to positive exponent

We know that \(a^{-n}=\frac{1}{a^{n}}\) (where \(a
eq0\) and \(n>0\)). So \(m^{-5}=\frac{1}{m^{5}}\)

Answer:

\(\frac{1}{m^{5}}\)