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