Divide :
`-50a^(2)b^(3)` by -`15a^(4)b^(2)`

Answer

To solve the problem of dividing \(-50a^{2}b^{3}\) by \(-15a^{4}b^{2}\), we can follow these steps:

### Step 1: Write the division as a fraction
We start by expressing the division in fraction form:
\[ \frac{-50a^{2}b^{3}}{-15a^{4}b^{2}} \]

### Step 2: Simplify the coefficients
Next, we simplify the numerical coefficients. The coefficients are \(-50\) and \(-15\). Since both are negative, they will cancel out:
\[ \frac{-50}{-15} = \frac{50}{15} = \frac{10}{3} \]

### Step 3: Simplify the variables
Now, we simplify the variable parts. We have \(a^{2}\) in the numerator and \(a^{4}\) in the denominator. According to the laws of exponents:
\[ \frac{a^{m}}{a^{n}} = a^{m-n} \]
So:
\[ \frac{a^{2}}{a^{4}} = a^{2-4} = a^{-2} \]

For the \(b\) terms, we have \(b^{3}\) in the numerator and \(b^{2}\) in the denominator:
\[ \frac{b^{3}}{b^{2}} = b^{3-2} = b^{1} = b \]

### Step 4: Combine the results
Now we can combine the simplified coefficients and variables:
\[ \frac{10}{3} \cdot a^{-2} \cdot b = \frac{10b}{3a^{2}} \]

### Final Answer
Thus, the final result of dividing \(-50a^{2}b^{3}\) by \(-15a^{4}b^{2}\) is:
\[ \frac{10b}{3a^{2}} \]

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