Question

simplify.
\frac{x^{5} z^{4}}{x^{2} z^{6}}

Explanation:

Step1: Simplify \( x \)-terms using exponent rule

For the \( x \)-terms, we use the rule \( \frac{a^m}{a^n}=a^{m - n} \). So for \( \frac{x^5}{x^2} \), we have \( x^{5 - 2}=x^3 \).

Step2: Simplify \( z \)-terms using exponent rule

For the \( z \)-terms, using the same rule \( \frac{a^m}{a^n}=a^{m - n} \), for \( \frac{z^4}{z^6} \), we get \( z^{4 - 6}=z^{-2} \), and \( z^{-2}=\frac{1}{z^2} \).

Step3: Combine the simplified terms

Combining the results from Step 1 and Step 2, we have \( \frac{x^3}{z^2} \).

Answer:

\(\frac{x^{3}}{z^{2}}\)