g) \( 2^{2 y-3}=8^{y+2} \)

To solve the equation \( 2^{2y - 3} = 8^{y + 2} \), we can express 8 as a power of 2. Since \( 8 = 2^3 \), we rewrite the equation: \[ 2^{2y - 3} = (2^3)^{y + 2} \] By applying the power of a power property, it simplifies to: \[ 2^{2y - 3} = 2^{3(y + 2)} \] Setting the exponents equal to each other gives us: \[ 2y - 3 = 3(y + 2) \] Now, distribute and solve for \( y \): \[ 2y - 3 = 3y + 6 \] \[ -3 - 6 = 3y - 2y \] \[ -9 = y \] Thus, the solution to the equation is \( y = -9 \). Fun fact for your brain: Exponents can feel a bit like magic—it's all about how you can turn numbers into powers! Whether you feel like a mathematician or just someone who loves a little number magic, mastering these tricks makes life a lot easier in both math and real-world problems. If you're looking to further level up your understanding of exponent rules, there are countless resources online and in libraries. Dive into books on algebra or even watch YouTube tutorials! Learning more about the properties of exponents can open up a whole new world of math mastery!