Full solution

\frac{24 x^{5} z^{2}}{12 x^{7} z}

Simplify Coefficients: Simplify the coefficients (numerical parts) of the expression. $\newline$ Divide $24$ by $12$ to simplify the coefficients. $\newline$ $24 / 12 = 2$
Simplify $x$ Terms: Simplify the $x$ terms by using the laws of exponents for division. $\newline$ Subtract the exponents of $x$ in the denominator from the exponents of $x$ in the numerator. $\newline$ $x^{5} / x^{7} = x^{5-7} = x^{-2}$
Simplify $z$ Terms: Simplify the $z$ terms by using the laws of exponents for division. $\newline$ Subtract the exponents of $z$ in the denominator from the exponents of $z$ in the numerator. $\newline$ $\frac{z^{2}}{z} = z^{2-1} = z^{1} = z$
Combine Results: Combine the results from Step $1$ , Step $2$ , and Step $3$ . The simplified expression is $2 \times x^{-2} \times z$ . However, $x^{-2}$ is not in its simplest form because it has a negative exponent.
Rewrite $x^{-2}$ : Rewrite $x^{-2}$ with a positive exponent by taking its reciprocal. $\newline$ $x^{-2} = 1 / x^{2}$
Final Simplified Expression: Combine the results from Step $4$ and Step $5$ to write the final simplified expression. $\newline$ The final simplified expression is $2 \times \left(\frac{1}{x^{2}}\right) \times z$ . $\newline$ This can be written as $\frac{2z}{x^{2}}$ .