Questions: When x, y, and z are positive integers, which of the following relationships will assure that the product x^0 y^1 z^-1 will have a value greater than 1 ? A. x<y B. x>y C. x>z D. y<z E. y>z

Solution Steps

To determine which relationship will assure that the product $x^{0} y^{1} z^{-1}$ will have a value greater than 1, we need to simplify the expression and analyze the conditions under which it holds true.

1. Simplify the expression $x^{0} y^{1} z^{-1}$ to $\frac{y}{z}$.
2. Determine the condition under which $\frac{y}{z} > 1$.

• Simplify the expression $x^{0} y^{1} z^{-1}$ to $\frac{y}{z}$.
• The product $\frac{y}{z}$ will be greater than 1 if $y > z$.

Given the expression $x^{0} y^{1} z^{-1}$, we can simplify it as follows: $$x^{0} y^{1} z^{-1} = 1 \cdot y \cdot \frac{1}{z} = \frac{y}{z}$$

We need to find the condition under which the product $\frac{y}{z}$ is greater than 1. This can be expressed mathematically as: $$\frac{y}{z} > 1$$

To solve the inequality $\frac{y}{z} > 1$, we multiply both sides by $z$ (assuming $z > 0$ since $z$ is a positive integer): $$y > z$$

Final Answer