Question

if $x \
eq 0$, then $\frac{x^9}{x^3}$ equals:
\bigcirc 1
\bigcirc 3
\bigcirc $x^2$
\bigcirc $x^3$
\bigcirc $x^6$
5 multiple choice 5 points
if x, y, and z are real non - zero numbers, then $\frac{x^8y^{10}z^2}{4x^3y^{15}z^3}$ is equivalent to:
\bigcirc $\frac{y^5z}{4x^5}$
\bigcirc $\frac{x^5z}{4x^3y^5}$
\bigcirc $\frac{x^5}{4x^3y^5z}$
\bigcirc $\frac{z}{4x^5y^5}$

Explanation:

Step1: Apply exponent rule for $x$

$\frac{x^9}{x^3}=x^{9-3}=x^6$

---

Step1: Simplify $x$-terms

$\frac{x^8}{x^3}=x^{8-3}=x^5$

Step2: Simplify $y$-terms

$\frac{y^{10}}{y^{15}}=y^{10-15}=y^{-5}=\frac{1}{y^5}$

Step3: Simplify $z$-terms

$\frac{z^2}{z^3}=z^{2-3}=z^{-1}=\frac{1}{z}$

Step4: Combine all terms

$\frac{x^5}{4y^5 z}=\frac{x^5}{4x^3 y^5 z}$ (matches the third option's structure)

Answer:

1. $\boldsymbol{x^6}$
2. $\boldsymbol{\frac{x^5}{4x^3 y^5 z}}$