Question

Решить 216^-2:6^-4×36^-2

Answer 1

$\tt 216^{-2}:6^{-4}\cdot36^{-2}=(6^3)^{-2}:6^{-4}\cdot(6^2)^{-2}=6^{-6}:6^{-4}\cdot6^{-4}=\\\\ =6^{-6-(-4)+(-4)}=6^{-6}=\cfrac{1}{6^6}$

Answer 2

To solve the expression, let's simplify each term step by step:

1. 216^-2: First, find the reciprocal of 216^2: 216^-2 = 1 / 216^2 = 1 / (216 * 216) = 1 / 46656 = 0.00002143347 (approximately)

2. 6^-4: Find the reciprocal of 6^4: 6^-4 = 1 / 6^4 = 1 / (6 * 6 * 6 * 6) = 1 / 1296 = 0.000771604938 (approximately)

3. 36^-2: Find the reciprocal of 36^2: 36^-2 = 1 / 36^2 = 1 / (36 * 36) = 1 / 1296 = 0.000771604938 (approximately)

Now, we have:

216^-2 : 6^-4 × 36^-2

Substitute the values we found:

0.00002143347 : 0.000771604938 × 0.000771604938

Now, perform the multiplication:

0.00002143347 : (0.000771604938)^2

Finally, evaluate the expression:

0.00002143347 : 0.0005950278644074074

Divide the two values:

Result ≈ 0.036006986402 (approximately)

So, 216^-2 : 6^-4 × 36^-2 is approximately equal to 0.036006986402.