Question

Вычислите: 21^8*27^5*49^6/9^11*343^7

Answer 1

$\frac{3}{7}$ или же 0,42

Answer 2

To calculate the expression, we can simplify it step by step:

1. Simplify the terms with the same base: 21^8 = (3 * 7)^8 = 3^8 * 7^8 27^5 = (3^3)^5 = 3^15 49^6 = (7^2)^6 = 7^12 9^11 = (3^2)^11 = 3^22 343^7 = 7^7

Now, the expression becomes:

(3^8 * 7^8) * (3^15) * (7^12) / (3^22) * (7^7)

2. Apply the rules of exponents (addition/subtraction of exponents when multiplying/dividing the same base):

3^8 * 3^15 = 3^(8+15) = 3^23 7^8 * 7^12 = 7^(8+12) = 7^20

So the expression becomes:

(3^23 * 7^20) / (3^22 * 7^7)

3. Now, divide the terms with the same base:

3^23 / 3^22 = 3^(23-22) = 3^1 = 3 7^20 / 7^7 = 7^(20-7) = 7^13

The final result is:

3 * 7^13