5) \( \frac{2^{2 n-3} \times\left(2^{n+2}\right)^{3}}{\left(2^{n+1}\right)^{5}} \)

Calculate or simplify the expression \( 2^{2n-3}*(2^(n+2))^3/(2^(n+1))^5 \). Simplify the expression by following steps: - step0: Solution: \(\frac{2^{2n-3}\left(2^{n+2}\right)^{3}}{\left(2^{n+1}\right)^{5}}\) - step1: Multiply the exponents: \(\frac{2^{2n-3}\times 2^{\left(n+2\right)\times 3}}{\left(2^{n+1}\right)^{5}}\) - step2: Multiply the terms: \(\frac{2^{2n-3}\times 2^{3\left(n+2\right)}}{\left(2^{n+1}\right)^{5}}\) - step3: Multiply the exponents: \(\frac{2^{2n-3}\times 2^{3\left(n+2\right)}}{2^{\left(n+1\right)\times 5}}\) - step4: Multiply by \(a^{-n}:\) \(2^{2n-3}\times 2^{3\left(n+2\right)}\times 2^{\left(-n-1\right)\times 5}\) - step5: Multiply the terms: \(2^{2n-3}\times 2^{3\left(n+2\right)}\times 2^{5\left(-n-1\right)}\) - step6: Multiply the terms: \(2^{2n-3+3\left(n+2\right)+5\left(-n-1\right)}\) - step7: Calculate: \(2^{-2}\) - step8: Express with a positive exponent: \(\frac{1}{2^{2}}\) - step9: Evaluate the power: \(\frac{1}{4}\) The simplified form of the expression \( \frac{2^{2n-3} \times\left(2^{n+2}\right)^{3}}{\left(2^{n+1}\right)^{5}} \) is \( \frac{1}{4} \) or 0.25.