Question

Find the simplified form of the expression. Give your answer in scientific notation. (9 x 105)(6 x 10-7)

Answer 1

We will initially rewrite the expression provided for the sake of clarity:

(9 x 10⁵)(6 x 10⁻⁷)

The simplify this type of expression, we must follow the order of operations. We can use the acronym BEDMAS to help us with this problem. BEDMAS refers to the order that mathematical operations take place and states that you first solve whatever is inside brackets (in this case parentheses). This is followed by addressing any exponents. After brackets and exponents it is division and multiplication that take place. Division and multiplication are interchangeable and can take place in either order. The same can be said for addition and subtraction which is the last operation, but each is interchangeable. Following these rules we can solve this expression:

We do not need to solve anything within the parentheses since we are asked to leave the problem in scientific notation. Scientific notation is of the form n x 10ˣ. We do not need to address the exponents either as they are a part of the scientific notation. Next we move on to multiplication which is multiplying the two numbers inside the parentheses.

(9 x 10⁵)(6 x 10⁻⁷)

We can multiply all of these terms in any order. To simplify, we can multiply both exponents as they have the same base numbers.

(9 x 6) (10⁵ x 10⁻⁷)
(54)(10⁻²)
54 x 10⁻²
5.4 x 10⁻¹

When multiplying exponents with the same base, we can add the exponents, and then multiply the rest of the terms and this provides us with option 2 as the answer.

Answer 2

9 x 10⁵ = 900000
6 x 10⁻⁷ = 0.0000006
900000 x 0.0000006 = 0.54
0.54 in scientific notation is = 5.4 x 10⁻¹