Solve for \( x \) \( 0.8^{(2 x+1)}=1 \)

Solve the equation \( 0.8^{(2x+1)}=1 \). Solve the equation by following steps: - step0: Solve for \(x\): \(0.8^{\left(2x+1\right)}=1\) - step1: Simplify: \(\left(\frac{4}{5}\right)^{2x+1}=1\) - step2: Write in exponential form: \(\left(\frac{4}{5}\right)^{2x+1}=\left(\frac{4}{5}\right)^{0}\) - step3: Set the exponents equal: \(2x+1=0\) - step4: Move the constant to the right side: \(2x=0-1\) - step5: Remove 0: \(2x=-1\) - step6: Divide both sides: \(\frac{2x}{2}=\frac{-1}{2}\) - step7: Divide the numbers: \(x=-\frac{1}{2}\) The solution to the equation \(0.8^{(2x+1)}=1\) is \(x=-\frac{1}{2}\) or \(x=-0.5\).