Question

Simplify the quantity negative 5 times a to the second power times b to the second power end quantity divided by the quantity 25 times a times b to the negative one power end quantity.

negative one times the quantity a times b to the third power end quantity divided by 5
−5ab3
negative a divided by the quantity 5 times b to the third power
negative one times the quantity 5 times a end quantity divided by b to the 3rd power

Answer 1

Let's simplify the expression step by step.

1. We're starting with the expression:
\[
\frac{-5a^2b^2}{25ab^{-1}}
\]

2. We can simplify the denominator:
\[
25ab^{-1} = 25a \cdot \frac{1}{b} = \frac{25a}{b}
\]

So the expression now looks like:
\[
\frac{-5a^2b^2}{\frac{25a}{b}} = \frac{-5a^2b^2 \cdot b}{25a} = \frac{-5a^2b^3}{25a}
\]

3. We can simplify further by canceling \(a\) in the numerator and denominator:
\[
\frac{-5ab^3}{25} = -\frac{5}{25} ab^3 = -\frac{1}{5} ab^3
\]

The simplified form of the original expression is:
\[
-\frac{1}{5} ab^3
\]

Now, matching it with the options provided, we find that:
- **Negative one times the quantity 5 times a end quantity divided by b to the 3rd power** simplifies out to: \(-\frac{5a}{b^3}\) which does not match.
- **Negative one times the quantity \(a \times b^3\) end quantity divided by 5** does similarly not match.
- **Negative a divided by the quantity 5 times b to the third power** which simplifies to: \(-\frac{a}{5b^3}\) which does not match as well.

The correct answer we deduced is not explicitly listed in the provided options, but the simplification is:
\[
-\frac{1}{5} ab^3
\]