Question

(1 7/9)^6× 6^12/8^10

Answer 1

(1 7/9)^6*6^12/8^10
(7/9)^6*2^12*3^12 / (2^3)^10
7^6/9^6*2^12*3^12/2^30
7^7/(3^2)^6*3^12/2^18
7^6/3^12*3^12/2^18
7^6*1/2^18
7^6/2^18

Answer 2

To simplify the expression, let's first convert the mixed number to an improper fraction:

1 7/9 = (9 * 1 + 7) / 9 = 16/9

Now, the expression becomes:

(16/9)^6 × 6^12 / 8^10

To calculate this, we can proceed step by step:

Step 1: Calculate (16/9)^6

(16/9)^6 = (16^6) / (9^6) = 16777216 / 531441 ≈ 31.52915957 (rounded to 8 decimal places)

Step 2: Calculate 6^12

6^12 = 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 = 2176782336

Step 3: Calculate 8^10

8^10 = 8 * 8 * 8 * 8 * 8 * 8 * 8 * 8 * 8 * 8 = 1073741824

Now, we can put it all together:

(16/9)^6 × 6^12 / 8^10 ≈ 31.52915957 × 2176782336 / 1073741824 ≈ 63985.998 (rounded to 3 decimal places)

So, the simplified value of the expression is approximately 63985.998.