To simplify the given expression, you need to apply laws of exponents. Let's solve it step by step:
1. Write down the given expression:
```
(2a^(5)b^(9)c^(-4))/(12a^(-8)b^(-7))
```
2. Solve inside the parenthesis on both the numerator and the denominator first. In this case, however, there's nothing to solve inside the parentheses.
3. Simplify the coefficients (i.e., the numbers in front of the variables) separately from the variables, if they can be simplified. Here, 2/12 simplifies to 1/6.
```
(1/6)a^(5)b^(9)c^(-4)/(a^(-8)b^(-7))
```
4. Apply the rule: a^(m)/a^(n) = a^(m - n). This rule applies to all variables present in the expression.
- For a: a^(5) / a^(-8) = a^(5 - (-8)) = a^(13)
- For b: b^(9) / b^(-7) = b^(9 - (-7)) = b^(16)
- There is no 'c' in the denominator to cancel out, so c^(-4) remains the same.
The expression now becomes:
```
(1/6)a^(13)b^(16)c^(-4)
```
5. Convert negative exponents: c^(-4) is equivalent to 1/c^(4). Using this property, rewrite the expression as:
```
(1/6)a^(13)b^(16) * 1/c^(4)
```
6. Since multiplication is commutative, we just organize terms so it looks nicer:
```
a^(13)b^(16)/(6c^(4))
```
This is the simplified expression of the original expression, with all exponents being positive.