Use the properties of exponents to simplify the following expression. Write the answer in scientific notation.
(5.6x10^5) (9.9x10^-8) divided by
(8.4x10^-4) (5x10^6)
=28.9x10^-1
I added 5.6 9.9 8.4 5
5+-8+-4+6+ -1
Oh my!!!
you are dealing with a multiplication and division of numbers, why are you adding them ?
your question:
(5.6x10^5) (9.9x10^-8) /( (8.4x10^-4) (5x10^6) )
= (5.6)(9.9)(10^-3) / ((8.4)(5)(10^2) )
= 55.44x10^-3 /(42 x 10^2)
= 1.32 x 10^-5
look at my solution line by line, and study what I did
remember that when dividing powers of the same base, we keep the base and subtract the exponents
so 10^-3 ÷ 10^2
= 10^(-3-2)
= 10^-5
To simplify the given expression using the properties of exponents and write the answer in scientific notation, we need to follow these steps:
Step 1: Multiply the numbers in the numerator and denominator.
(5.6x10^5) (9.9x10^-8) = 5.6 * 9.9 * 10^5 * 10^-8
= 55.44 * 10^(-3)
Step 2: Divide the numerator by the denominator.
(55.44 * 10^(-3)) / ((8.4x10^-4) (5x10^6))
Now, let's simplify the denominator separately.
(8.4x10^-4) (5x10^6) = 8.4 * 5 * 10^(-4+6)
= 42 * 10^2 = 4200
Now, divide the numerator (55.44 * 10^(-3)) by the denominator (4200).
(55.44 * 10^(-3)) / 4200 = 0.0132 * 10^(-3)
Step 3: Simplify the result into scientific notation.
0.0132 * 10^(-3) = 1.32 * 10^(-2-3) = 1.32 * 10^-5
Therefore, the simplified expression in scientific notation is 1.32 * 10^-5.
To simplify the expression using the properties of exponents, you need to perform the appropriate operations on both the coefficients and the exponents separately.
Let's break down the given expression step-by-step:
(5.6x10^5) (9.9x10^-8) divided by (8.4x10^-4) (5x10^6)
First, multiply the coefficients:
5.6 * 9.9 = 55.44
Next, multiply the powers of 10:
10^5 * 10^-8 = 10^(5-8) = 10^-3
Now divide the coefficients:
55.44 / (8.4 * 5) = 55.44 / 42 = 1.319
Lastly, subtract the exponents of 10:
10^-3 * 10^(6+4) = 10^(6+4-3) = 10^7
Putting it all together, the simplified expression in scientific notation is:
1.319x10^7