Question

1)(3^3)^3×5^7×2^2/81^2×10^5 2)(6^3)^3×9^2×(5^3)^2/1000×18^7​

Answer 1

Решение во вложении:

Answer 2

Let's simplify the given expressions step by step:

1. (3^3)^3 × 5^7 × 2^2 / 81^2 × 10^5

First, let's simplify the exponents within parentheses:

(3^3)^3 = 3^(3 × 3) = 3^9

Now, let's simplify the expression:

3^9 × 5^7 × 2^2 / 81^2 × 10^5

Next, let's simplify the terms with the same base:

3^9 / 81^2 = (3^9) / (9^2) = (3^9) / (3^4 × 3^4) = 3^(9 - 4 - 4) = 3^1 = 3

Now, the expression becomes:

3 × 5^7 × 2^2 × 10^5

Next, let's simplify the remaining terms:

5^7 × 2^2 = 5^7 × 4 = (5^2)^3 × 4 = 25^3 × 4

10^5 = 10^2 × 10^3 = 100 × 1000 = 100000

Now, the expression becomes:

3 × 25^3 × 4 × 100000

Finally, let's evaluate the expression:

3 × 25^3 × 4 × 100000 = 3 × 15625 × 4 × 100000 = 1875000000

Therefore, the result is 1,875,000,000.

2. (6^3)^3 × 9^2 × (5^3)^2 / 1000 × 18^7

First, let's simplify the exponents within parentheses:

(6^3)^3 = 6^(3 × 3) = 6^9

(5^3)^2 = 5^(3 × 2) = 5^6

Now, let's simplify the expression:

6^9 × 9^2 × 5^6 / 1000 × 18^7

Next, let's simplify the terms with the same base:

6^9 / 18^7 = (6^3)^3 / (6^1 × 3^7) = 6^(3 × 3 - 1 - 7) = 6^2 = 36

1000 = 10^3

Now, the expression becomes:

36 × 9^2 × 5^6 / 10^3

Next, let's simplify the remaining terms:

9^2 = 81

5^6 = 5^2 × 5^2 × 5^2 = 25 × 25 × 25 = 15625

10^3 = 1000

Now, the expression becomes:

36 × 81 × 15625 / 1000

Finally, let's evaluate the expression:

36 × 81 × 15625 / 1000 = 45000000

Therefore, the result is 45,000,000.