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(4.2 x 10^3)(1.5 x 10^6)

I need help. I dont know how to get the anwser to this math question. I need to do either properties of exponents which are product of powers, power of a power, power of a product, negatvie exponent, zero exponent, quotient of powers, power of a quotient. Please Help

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Hi, I am not sure why my answers are not reaching the screen but you would use the product of powers property by multiplying all the exponential numbers with base 10. The way you do this is to add the powers 6 and 3. Multiply the numbers 1.5 and 4.2. 

Your answer should be 6.3 x 10^9

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4 Answers

 Just simply use the Commutative property of multiplication( changing order of factors(.
 
    abcd = acbd = acdb = bacd = badc = ......
 
    Do and group them together
 
    ( 4.2 X 106) ( 1.5 x 103 ) =( 4.2 X 1.5 ) 109 = 6.3 X 106
  Don't even need to have all these steps.

Hello Diaraliz,

If (4.2 x 10^3)(1.5 x 10^6) is written as 4200 *1500000 does it look more familiar?

everything in (4.2 x 10^3)(1.5 x 10^6) is multiplied together so you can regroup the 10's and their powers together  and group the coeficients also.  Like this:

(4.2 * 1.5 )(10^3  * 10^6 )  

6.3  * (10^3 * 10^6 )

Multiplcation of terms with numbers with exponents is done by adding the exponents

6.3 * (10^9)

Check:  what is the result of 4200 *1500000?

4200 *1500000 = 6300000000  => 6.3*10^9

Good Luck!  BruceS

 

Rizul is correct - here's what it looks like:

(4.2 * 1.5) (103 * 106) = 6.3 * 109.  Exponents simply add when you multiply

Example:  22 = 4 (2*2), and 23 = 8 (2*2*2)

4 * 8 = 32;  so does 2* 23      (2*2)(2*2*2) = 32

If you have an exponent raised to another exponent (example:  (22)3 = 26 = 64

= (2*2) (2*2) (2*2) = 64

103 and 106 have exponents and the same base (10). Whenever you are multiplying these types of numbers you know you will have to do product of powers property

(4.2 x 103)(1.5 x 106)

(4.2 x 1.5) (103 x 106)       Use product of powers to solve second parenthesis. Multiply the

                                           numbers in the first parenthesis

(6.3)(106+3)                      Product of powers mean that given two exponential numbers with

                                          same base (10 in this case) multiplying each other, simply add their

                                          two powers

6.3 x 109                                     Leave your answer in this scientific notation since simplifying will

                                          get you 6300000000. We avoid this often in math