Q. 184 - Intermediate Algebra

Question

In the following exercises, simplify.

a.$(-4\sqrt{5})\left(5\sqrt{10}\right)$

b.$(-2\sqrt[3]{9})\left(7\sqrt[3]{9}\right)$

Step-by-Step Solution

Answer

On multiplication, we get $-100\sqrt{2},-42\sqrt[3]{9}$ respectively

Part (a) Step 1: Given information

Given the expression $(-4\sqrt{5})\left(5\sqrt{10}\right),(-2\sqrt[3]{9})\left(7\sqrt[3]{9}\right)$

Part (a) Step 2: Multiplying the terms and simplifying

Multiplying the terms and simplifying, we get, we get

$$\begin{gathered} (-4\sqrt{5})\left(5\sqrt{10}\right)=(-4.5)(\sqrt{5}.\sqrt{10}) \\ (-4\sqrt{5})\left(5\sqrt{10}\right)=-20(\sqrt{5}.\sqrt{5}.\sqrt{2}) \\ (-4\sqrt{5})\left(5\sqrt{10}\right)=-20\left(5\sqrt{2}\right) \\ (-4\sqrt{5})\left(5\sqrt{10}\right)=-100\sqrt{2} \end{gathered}$$

Part (b) Step 1: Given information

Given expression $(-2\sqrt[3]{9})\left(7\sqrt[3]{9}\right)$

Part (b) Step 2: Multiplying and simplifying

Multiplying, we get

$$\begin{gathered} (-2\sqrt[3]{9})\left(7\sqrt[3]{9}\right)=(-2·7)(\sqrt[3]{9}·\sqrt[3]{9}) \\ (-2\sqrt[3]{9})\left(7\sqrt[3]{9}\right)=-14·\sqrt[3]{81} \\ (-2\sqrt[3]{9})\left(7\sqrt[3]{9}\right)=-14·\sqrt[3]{27·3} \\ (-2\sqrt[3]{9})\left(7\sqrt[3]{9}\right)=-14·\sqrt[3]{27}·\sqrt[3]{3} \\ (-2\sqrt[3]{9})\left(7\sqrt[3]{9}\right)=-14·\sqrt[3]{(3{)}^3}·\sqrt[3]{3} \\ (-2\sqrt[3]{9})\left(7\sqrt[3]{9}\right)=-14·3·\sqrt[3]{9} \\ (-2\sqrt[3]{9})\left(7\sqrt[3]{9}\right)=-42\sqrt[3]{9} \end{gathered}$$