Question

0,5m²n•(4mn³)² упостить

Answer 1

$0.5m {}^{2} n \times (4mn {}^{3}) { {}^{} }^{2} \\ 4 {}^{2} m {}^{2} \times (n {}^{3} ) {}^{2} \\0.5m {}^{2}n \times 16m {}^{2} n {}^{6} \\ 8m {}^{2} nm {}^{2} n {}^{6} \\ 8m {}^{2 + 2} n \times n {}^{6} \\ 8m {}^{4} n {}^{1} \times n {}^{1 + 6} \\ 8m {}^{4} n {}^{7}$

Answer 2

To simplify the expression 0.5m²n • (4mn³)², we'll perform the necessary calculations and simplify any powers.

Step 1: Calculate the power (4mn³)² (4mn³)² = 4² * (m²)² * (n³)² = 16 * m^(22) * n^(32) = 16 * m^4 * n^6

Step 2: Substitute the simplified power back into the expression: 0.5m²n • (4mn³)² = 0.5m²n • (16m^4n^6)

Step 3: Multiply the constants (0.5 and 16): 0.5 * 16 = 8

Step 4: Multiply the variables with the same base (m and m^4): m² * m^4 = m^(2+4) = m^6

Step 5: Multiply the variables with the same base (n and n^6): n * n^6 = n^(1+6) = n^7

Step 6: Combine the results: 8 * m^6 * n^7

So, the simplified expression is 8m^6n^7.