## Answer :

**Simplify the algebraic expression:**

We are given the expression:

[tex]\[ 4a^2 b^3 \times 5bc^3 \div 10ab^2c \][/tex]

First, we handle the multiplication in the numerator:

[tex]\[ 4a^2 b^3 \times 5bc^3 = (4 \times 5) \times a^2 \times b^3 \times b \times c^3 = 20a^2 b^4 c^3 \][/tex]

Now, we perform the division:

[tex]\[ \frac{20a^2 b^4 c^3}{10ab^2c} \][/tex]

We can simplify this by dividing both the numerator and the denominator:

1. [tex]\( \frac{20}{10} = 2 \)[/tex]

2. [tex]\( \frac{a^2}{a} = a \)[/tex]

3. [tex]\( \frac{b^4}{b^2} = b^2 \)[/tex]

4. [tex]\( \frac{c^3}{c} = c^2 \)[/tex]

So, the simplified expression is:

[tex]\[ 2ab^2c^2 \][/tex]

**How much more did Tapaba receive compared to Palibe:**

Palibe and Tapaba shared [tex]$30.00 in the ratio \(2:3\) respectively. To find out how much more Tapaba received compared to Palibe, we proceed as follows: 1. Calculate the total parts of the ratio: \[ 2 + 3 = 5 \] 2. Determine the amount each part represents: \[ \text{One part} = \frac{30.00}{5} = 6.00 \] 3. Calculate the amount received by Palibe (2 parts): \[ \text{Amount received by Palibe} = 2 \times 6.00 = 12.00 \] 4. Calculate the amount received by Tapaba (3 parts): \[ \text{Amount received by Tapaba} = 3 \times 6.00 = 18.00 \] 5. Find the difference between the amounts received by Tapaba and Palibe: \[ \text{Difference} = 18.00 - 12.00 = 6.00 \] Therefore, Tapaba received $[/tex]6.00 more than Palibe.