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

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

# 4 Answers

^{6}) ( 1.5 x 10

^{3}) =( 4.2 X 1.5 ) 10

^{9 }= 6.3 X 10

^{6}

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) (10^{3} * 10^{6}) = 6.3 * 10^{9}. Exponents simply add when you multiply

Example: 2^{2} = 4 (2*2), and 2^{3} = 8 (2*2*2)

4 * 8 = 32; so does 2^{2 }* 2^{3} (2*2)(2*2*2) = 32

If you have an exponent raised to another exponent (example: (2^{2})^{3} = 2^{6} = 64

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

10^{3} and 10^{6} 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 10 ^{3})(1.5 x 10^{6})**

**(4.2 x 1.5) (10 ^{3} x 10^{6}) Use product of powers to solve second parenthesis. Multiply the
**

** numbers in the first parenthesis**

**(6.3)(10 ^{6+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 10 ^{9 }Leave your answer in this scientific notation since simplifying will
**

** get you ****6300000000. We avoid this often in math**

## Comments

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

Thank you very much

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