Question

Question 3(Multiple Choice Worth 1 points)
(06.03 LC)

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

To simplify the expression \(-5a^2b^2\) divided by \(25ab^{-1}\), we can follow these steps:

1. Write the expression as a fraction:

\[
\frac{-5a^2b^2}{25ab^{-1}}
\]

2. Simplify the coefficients and variables separately:

- First, simplify the coefficients: \(-5\) divided by \(25\) is \(-\frac{5}{25} = -\frac{1}{5}\).

- Next, simplify the \(a\) terms: \(a^2\) divided by \(a\) is \(a^{2-1} = a^1 = a\).

- Now simplify the \(b\) terms: \(b^2\) divided by \(b^{-1}\) is \(b^{2 - (-1)} = b^{2 + 1} = b^3\).

3. Putting this all together, we have:

\[
\frac{-5a^2b^2}{25ab^{-1}} = -\frac{1}{5}ab^3
\]

This matches one of the choices provided.

The simplified expression is therefore:

\[
-\frac{1}{5}ab^3
\]

So, the correct multiple choice answer would be:

**negative one times the quantity a times b to the third power end quantity divided by 5**.