Sure, let's solve this step by step:

(0.000064)^(-5/6)

To find the value of this expression, we first need to take the reciprocal of the base (0.000064), and then raise it to the power of (-5/6).

Step 1: Reciprocal

Reciprocal of 0.000064 is 1/0.000064 = 15625

Step 2: Exponentiation

Now, we need to raise 15625 to the power of (-5/6):

(15625)^(-5/6)

To calculate this, you can find the sixth root of 15625 and then raise it to the power of -5:

(15625^(1/6))^(-5)

Step 3: Calculate the sixth root

(15625^(1/6)) is approximately 5 because 5^6 = 15625.

Step 4: Raise to the power of -5

Now, we have:

(5)^(-5)

Step 5: Calculate

To calculate (5)^(-5), you take the reciprocal of 5 raised to the 5th power:

1 / (5^5)

1 / (5 * 5 * 5 * 5 * 5) = 1 / 3125

So, the value of (0.000064)^(-5/6) is approximately 0.00032 (rounded to five decimal places).