Question

simplify.
\\(\frac{a b^{7} z^{6}}{a^{4} b^{5}}\\)

Explanation:

Step1: Simplify \(a\) terms

Use the rule \(\frac{x^m}{x^n}=x^{m - n}\). For \(a\): \(m = 1\), \(n = 4\), so \(a^{1-4}=a^{-3}=\frac{1}{a^3}\).

Step2: Simplify \(b\) terms

For \(b\): \(m = 7\), \(n = 5\), so \(b^{7 - 5}=b^{2}\).

Step3: Simplify \(z\) terms

\(z\) has no denominator term, so \(z^{6}\) remains.

Step4: Combine terms

Multiply the simplified terms: \(\frac{1}{a^3}\times b^{2}\times z^{6}=\frac{b^{2}z^{6}}{a^3}\).

Answer:

\(\frac{b^{2}z^{6}}{a^{3}}\)