**Simplifying the Expression:**

To simplify the given expression, we'll follow the order of operations (PEMDAS/BODMAS) and perform the necessary calculations step by step.

**Step 1: Simplify the Numerator**

The numerator of the expression is: 3^(-6) × 45 × 5^2 × t^(-8)

To simplify this, we'll calculate the powers first:

3^(-6) = 1 / 3^6 = 1 / (3 × 3 × 3 × 3 × 3 × 3) = 1 / 729

5^2 = 5 × 5 = 25

Now, we can rewrite the numerator as:

1 / 729 × 45 × 25 × t^(-8)

**Step 2: Simplify the Denominator**

The denominator of the expression is: 125 × 27 × t^(-4)

Again, we'll calculate the powers first:

t^(-4) = 1 / t^4 = 1 / (t × t × t × t) = 1 / (t^4)

Now, we can rewrite the denominator as:

125 × 27 × 1 / (t^4)

**Step 3: Simplify the Whole Expression**

Now that we have simplified the numerator and denominator separately, we can divide the numerator by the denominator:

(1 / 729 × 45 × 25 × t^(-8)) ÷ (125 × 27 × 1 / (t^4))

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

(1 / 729 × 45 × 25 × t^(-8)) × (1 / (125 × 27 × 1 / (t^4))) = (1 / 729 × 45 × 25 × t^(-8)) × (1 / (125 × 27 / (t^4)))

Next, we'll simplify the expression further by multiplying the numerators and denominators together:

(1 × 45 × 25 × t^(-8)) ÷ (729 × 125 × 27 / t^4)

Multiplying the numbers:

45 × 25 = 1125

Multiplying the variables with negative exponents:

t^(-8) ÷ t^4 = 1 / (t^8 × t^4) = 1 / t^(8+4) = 1 / t^12

Now we can rewrite the expression as:

1125 / (729 × 125 × 27 / t^12)

**Step 4: Further Simplification**

To simplify the expression even further, we'll multiply the numbers in the denominator:

729 × 125 × 27 = 729 × 3375 = 245,887,875

Now we can rewrite the expression as:

1125 / (245,887,875 / t^12)

To divide by a fraction, we multiply by the reciprocal:

1125 × (t^12 / 245,887,875)

Finally, we have the simplified expression:

1125t^12 / 245,887,875