Question

The length of a rectangle is 4a^4 • b^5 and the width is 3a^2 • b^3 what is the expression that represents the area of the rectangle?

Answer 1

The expression for area of rectangle is:
`\mathbf{Area\: of\: Rectangle=12a^6b^8}`

Explanation:

Length of Rectangle =
`4a^4\: .\: b^5`

Width of Rectangle =
`3a^2\: .\: b^3`

We need to find Area of Rectangle.

The formula used is:
`Area\: of\: Rectangle=Length* Width`

Putting values of length and width and finding area

`Area\: of\: Rectangle=Length* Width\\Area\: of\: Rectangle=(4a^4 . b^5)* (3a^2 \:.\: b^3)`

We will multiply constants with constants and same variables

`Area\: of\: Rectangle=(4)(3)a^4(a^2) b^5(b^3)\\Area\: of\: Rectangle=12a^(4+2)b^(5+3)\\Area\: of\: Rectangle=12a^6b^8`

So, The expression for area of rectangle is:
`\mathbf{Area\: of\: Rectangle=12a^6b^8}`