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

Question

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

Answer 1

 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.

Answer 2

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

 

Answer 3

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 2² * 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

Answer 4

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