Question

what is the ratio of the height of this solid cylindrical rod to its diameter, in simplified form?
ratio of the height of the solid cylindrical rod to its diameter.
____ to 1

Explanation:

Step1: Identify given values

Height = $x^5y^{10}z$, Diameter = $xy^7$

Step2: Set up the ratio

$\text{Ratio} = \frac{\text{Height}}{\text{Diameter}} = \frac{x^5y^{10}z}{xy^7}$

Step3: Simplify using exponent rules

For $x$: $x^{5-1}=x^4$; For $y$: $y^{10-7}=y^3$; $z$ remains.
$\frac{x^5y^{10}z}{xy^7} = x^4y^3z$

Answer:

$\boldsymbol{x^4y^3z}$ to 1