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

Answer:

$\boxed{6.432 \times 10^{5}}$

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:

$800 \rightarrow 8 \times 10^2$

Or:

$5,700,000,000 \rightarrow 5.7 \times 10^9$

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

$(9.6 \times 10^3) \times (6.7 \times 10^2)$

• By Associative Property:

$(9.6 \times 10^3) \times (6.7 \times 10^2)=(9.6 \times 6.7 \times 10^3 \times 10^2$

$(9.6 \times 10^3) \times (6.7 \times 10^2)=(9.6 \times 6.7 \times 10^3 \times 10^2) \\ \\ = 64.32 \times 10^3 \times 10^2$

• By Product of Powers Property:

Same base 10 and adding exponents:

$64.32 \times 10^{3+2}=64.32 \times 10^{5} \\ \\ Arranging:\\ \\ \boxed{6.432 \times 10^{6}}$