Multiply :
`-(2)/(3)a^(7)b^(2)` and `-(9)/(4)ab^(5)`

Answer

To multiply the expressions \(-\frac{2}{3}a^{7}b^{2}\) and \(-\frac{9}{4}ab^{5}\), we will follow these steps:

### Step 1: Multiply the coefficients
We start by multiplying the coefficients of the two expressions:
\[ -\frac{2}{3} \times -\frac{9}{4} \]
Since both coefficients are negative, the product will be positive.

### Step 2: Calculate the product of the coefficients
Calculating the product:
\[ \frac{2 \times 9}{3 \times 4} = \frac{18}{12} \]
Now simplify \(\frac{18}{12}\):
\[ \frac{18 \div 6}{12 \div 6} = \frac{3}{2} \]

### Step 3: Multiply the variables
Next, we multiply the variable parts:
1. For \(a\):
\[ a^{7} \times a = a^{7+1} = a^{8} \]
2. For \(b\):
\[ b^{2} \times b^{5} = b^{2+5} = b^{7} \]

### Step 4: Combine the results
Now, we combine the results from the coefficients and the variables:
\[ \frac{3}{2}a^{8}b^{7} \]

### Final Answer
Thus, the final result of the multiplication is:
\[ \frac{3}{2}a^{8}b^{7} \]

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