(8 x 10^3)(10^4)/(5 x 10^-1)(1 x 10^-2)

Question

(8 x 10^3)(10^4)/(5 x 10^-1)(1 x 10^-2)

Simplify and give your answer in scientific notation.

Answer 1

Hi Paige!

 

Let's go over two rules of exponents first. 

1.  If you have (10^a)(10^b) because the bases are the same (which in this case the base is 10) the exponents can be added together resulting in 10^(a+b).

 

2.  If you have division, (10^a)/(10^b) since the bases are the same (again base 10) the exponent in the numerator is subtracted from the exponent in the denominator resulting in 10^(a-b).

 

Now to simplify your question:

Let's start with the numerator:    (8 x 10^3)(10^4)  = 8 x (10^3)(10^4) = 8 x 10^(3+4)= 8 x 10^7

 

Keeping in mind the commutative law of multiplication, now the denominator:   

(5 x 10^-1)(1 x 10^-2) =  5 (1) x (10^-1)(10^-2) = 5 x  10^(-1+-2)= 5 x 10^-3

 

So far we have simplified the expression to:  (8 x 10^7)/(5 x 10^-3)

Now use rule #2:     8/5  x  (10^7)/(10^-3) =  8/5 x 10^(7- -3) = 8/5 x (10^10)

 

Since the final answer needs to be in scientific notation, you must change the fraction 8/5 into a decimal:  8/5 = 1.6

 

So, 8/5 x (10^10) = 1.6 x 10^10    

 

Hope that my explanation helps you understand the process.

THINK MATH!!