Multiply :
`(2)/(3)ab` by `-(1)/(4)a^(2)b`

Answer

To solve the problem of multiplying \(\frac{2}{3}ab\) by \(-\frac{1}{4}a^{2}b\), we will follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ \frac{2}{3}ab \times -\frac{1}{4}a^{2}b \]

### Step 2: Multiply the coefficients
Next, we multiply the coefficients (the numerical parts):
\[ \frac{2}{3} \times -\frac{1}{4} = -\frac{2 \times 1}{3 \times 4} = -\frac{2}{12} = -\frac{1}{6} \]

### Step 3: Multiply the variables
Now, we multiply the variable parts. We have:
\[ ab \times a^{2}b \]
Using the laws of exponents, we can combine the \(a\) terms and the \(b\) terms:
\[ a^{1} \times a^{2} = a^{1+2} = a^{3} \]
\[ b^{1} \times b^{1} = b^{1+1} = b^{2} \]

### Step 4: Combine the results
Now we combine the results from the coefficients and the variables:
\[ -\frac{1}{6} a^{3} b^{2} \]

### Final Answer
Thus, the final answer is:
\[ -\frac{1}{6} a^{3} b^{2} \]

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