Question

Use the Associative Property and the Product of Powers Property

to simplify the expression below. Express your answer in scientific
notation. Show your work
(9.6 x 103) × (6.7 x 10²​

Answer 1

`\boxed{6.432 * 10^(5)}`

Step-by-step explanation:

We use Scientific Notation as a special way of writing numbers. It is an amazing way to represent both big and small numbers, like this:

`800 \rightarrow 8 * 10^2`

Or:

`5,700,000,000 \rightarrow 5.7 * 10^9`

So in this exercise, we need to us Associative Property and the Product of Powers Property to find the result of:

`(9.6 * 10^3) * (6.7 * 10^2)`

• By Associative Property:

`(9.6 * 10^3) * (6.7 * 10^2)=(9.6 * 6.7 * 10^3 * 10^2 \\ \\`

`(9.6 * 10^3) * (6.7 * 10^2)=(9.6 * 6.7 * 10^3 * 10^2) \\ \\ = 64.32 * 10^3 * 10^2`

• By Product of Powers Property:

Same base 10 and adding exponents:

`64.32 * 10^(3+2)=64.32 * 10^(5) \\ \\ Arranging:\\ \\ \boxed{6.432 * 10^(6)}`