Question

(2⁶)⁵×{3⁴×28‐[3‐(2³×5³‐3²×10²‐5²):(1+4)²]:10⁴‐1×3⁴} va rog cu tot procesul de rezolvare MULTUMESC!!!​

Answer 1

$\left(2^6\right)^5\cdot\left\{3^4\cdot28-\left[3-\left(2^3\cdot 5^3-3^2\cdot 10^2-5^2\right):(1+4)^2\right]:10^4-1\cdot 3^4\right\}=\\ \\ =2^{5\cdot 6}\cdot\left\{3^4\cdot 28-\left[3-\left(\left(2\cdot 5\right)^3-3^2\cdot 10^2-5^2\right):5^2\right]:10^4-3^4\right\}\\ \\ =2^{30}\cdot \left\{3^4\cdot 28-\left[3-\left(10^3-9\cdot 10^2-5^2\right):5^2\right]:10^4-3^4\right\}$

$=2^{30}\cdot \left\{3^4\cdot 28-\left[3-\left(10^2\cdot \left(10-9\right)-5^2\right):5^2\right]:10^4-3^4\right\}\\ \\ = 2^{30}\cdot \left\{3^4\cdot 28 - \left[3-\left(10^2-5^2\right):5^2\right]:10^4-3^4\right\}$

$=2^{30}\cdot \left\{3^4\cdot 28 - \left[3-\left(10-5\right)\left(10+5\right):5^2\right]:10^4-3^4\right\}\\ \\=2^{30}\cdot \left[3^4\cdot 28 - \left(3-5\cdot 15:5^2\right):10^4-3^4\right]$

$= 2^{30}\cdot \left[3^4\cdot 28 - \left(3-5\cdot 5\cdot 3:5^2\right):10^4-3^4\right]\\ \\ = 2^{30}\cdot \left[3^4\cdot 28 - \left(3-3\right):10^4-3^4\right]\\ \\ = 2^{30}\cdot \left(3^4\cdot 28-0:10^4-3^4\right)\\ \\ =2^{30}\cdot \left(3^4\cdot 28-3^4\right)\\ \\ = 2^{30}\cdot \left[3^4\cdot \left(28-1\right)\right]\\ \\ = 2^{30}\cdot \left(3^4\cdot 27\right)\\ \\ = 2^{30}\cdot\left(3^4\cdot 3^{3}\right)\\ \\ = 2^{30}\cdot 3^{4+3}\\ \\ = \boxed{2^{30}\cdot 3^7}$