524. Förenkla och skriv ut talet. \( \begin{array}{ll}\text { a) }\left(10^{2}\right)^{3} \cdot 10^{4} & \text { b) } 10^{3} \cdot 10^{-5} \cdot 10^{8} \\ \text { c) } 10^{-3} \cdot\left(10^{3}\right)^{2} & \text { d) } 10^{4} \cdot\left(10^{-2}\right)^{3}\end{array} \)

Calculate the value by following steps: - step0: Calculate: \(10^{-3}\left(10^{3}\right)^{2}\) - step1: Multiply the exponents: \(10^{-3}\times 10^{3\times 2}\) - step2: Multiply the numbers: \(10^{-3}\times 10^{6}\) - step3: Multiply: \(10^{-3+6}\) - step4: Add the numbers: \(10^{3}\) - step5: Evaluate the power: \(1000\) Calculate or simplify the expression \( (10^2)^3 * 10^4 \). Calculate the value by following steps: - step0: Calculate: \(\left(10^{2}\right)^{3}\times 10^{4}\) - step1: Multiply the exponents: \(10^{2\times 3}\times 10^{4}\) - step2: Multiply the numbers: \(10^{6}\times 10^{4}\) - step3: Multiply: \(10^{6+4}\) - step4: Add the numbers: \(10^{10}\) Calculate or simplify the expression \( 10^3 * 10^{-5} * 10^8 \). Calculate the value by following steps: - step0: Calculate: \(10^{3}\times 10^{-5}\times 10^{8}\) - step1: Multiply the terms: \(10^{3-5+8}\) - step2: Calculate: \(10^{6}\) Calculate or simplify the expression \( 10^4 * (10^{-2})^3 \). Calculate the value by following steps: - step0: Calculate: \(10^{4}\left(10^{-2}\right)^{3}\) - step1: Multiply the exponents: \(10^{4}\times 10^{-2\times 3}\) - step2: Multiply the numbers: \(10^{4}\times 10^{-6}\) - step3: Multiply: \(10^{4-6}\) - step4: Subtract the numbers: \(10^{-2}\) - step5: Express with a positive exponent: \(\frac{1}{10^{2}}\) - step6: Evaluate the power: \(\frac{1}{100}\) Här är förenklingarna av de givna uttrycken: a) \( (10^{2})^{3} \cdot 10^{4} \) Förenkling: \[ (10^{2})^{3} = 10^{2 \cdot 3} = 10^{6} \] Därefter: \[ 10^{6} \cdot 10^{4} = 10^{6 + 4} = 10^{10} \] **Resultat:** \( 10^{10} \) --- b) \( 10^{3} \cdot 10^{-5} \cdot 10^{8} \) Förenkling: \[ 10^{3} \cdot 10^{-5} \cdot 10^{8} = 10^{3 - 5 + 8} = 10^{6} \] **Resultat:** \( 10^{6} \) eller \( 1000000 \) --- c) \( 10^{-3} \cdot (10^{3})^{2} \) Förenkling: \[ (10^{3})^{2} = 10^{3 \cdot 2} = 10^{6} \] Därefter: \[ 10^{-3} \cdot 10^{6} = 10^{-3 + 6} = 10^{3} \] **Resultat:** \( 1000 \) --- d) \( 10^{4} \cdot (10^{-2})^{3} \) Förenkling: \[ (10^{-2})^{3} = 10^{-2 \cdot 3} = 10^{-6} \] Därefter: \[ 10^{4} \cdot 10^{-6} = 10^{4 - 6} = 10^{-2} \] **Resultat:** \( 10^{-2} \) eller \( 0.01 \) --- Sammanfattning av resultaten: - a) \( 10^{10} \) - b) \( 10^{6} \) eller \( 1000000 \) - c) \( 1000 \) - d) \( 10^{-2} \) eller \( 0.01 \)