
Diaraliz C.
asked 01/06/13(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
4 Answers By Expert Tutors

Parviz F. answered 09/15/13
Mathematics professor at Community Colleges

BRUCE S. answered 01/06/13
Learn & Master Physics & Math with Bruce S
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

Bill F. answered 01/06/13
Experienced Teacher & Tutor in Round Rock, TX
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

Rizul N. answered 01/06/13
UNC-CH Grad For Math and Science Tutor
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
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Rizul N.
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
01/06/13