Question

If \[ \left( \frac{2}{1} \right)^x \left( \frac{-1}{1} \right)^y = \left( \frac{4}{5} \right), \] then find the value of \( 2x - 3y \).

• A. 1
• B. -1
• C. 2
• D. 0

Hint:

In equations involving powers, consider the properties of exponents and solve for each variable individually.

Answer 1

The Correct Option is D

From the given equation, we have: \[ \left( \frac{2}{1} \right)^x \left( \frac{-1}{1} \right)^y = \left( \frac{4}{5} \right). \] This simplifies to: \[ 2^x \times (-1)^y = \frac{4}{5}. \] Since \( (-1)^y \) can only be 1 or -1, this equation only holds if \( y \) is even and \( 2^x = \frac{4}{5} \). Solving for \( x \) and \( y \), we find that the equation holds when \( x = 0 \) and \( y = 0 \), which gives: \[ 2x - 3y = 2(0) - 3(0) = 0. \]