Question

simplify the expression. assume (\frac{4z^{0}}{32z^{-7}})

Explanation:

Step1: Simplify the coefficient and use the zero - exponent rule

The zero - exponent rule states that for any non - zero number \(a\), \(a^{0}=1\). So \(z^{0} = 1\) (assuming \(z
eq0\)). Also, simplify the fraction of the coefficients: \(\frac{4}{32}=\frac{1}{8}\). The expression becomes \(\frac{1\times1}{8z^{-7}}=\frac{1}{8z^{-7}}\)

Step2: Use the negative - exponent rule

The negative - exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\) (for \(a
eq0\)) and \(\frac{1}{a^{-n}}=a^{n}\). So \(\frac{1}{z^{-7}} = z^{7}\). Then the expression \(\frac{1}{8z^{-7}}\) becomes \(\frac{z^{7}}{8}\)

Answer:

\(\frac{z^{7}}{8}\)