problems with exponents?

Question

(2 x 10^4)times(2 x 10^-6)

(4 x 10^2)/(2 x 10^-3)

(6 x 10^12)+(5 x 10^11)

(4 x 10^15)-(2 x 10^13)

can you please show your work

Answer 1

When multiplying or dividing use these rules:

Rule 1 if the bases are the same you can add the exponents.
Rule 2 flip the sign of the power when you move it.

in problem 1 you have two tens (similar bases) with powers of 4 and -6 which becomes 4 + -6 when added to get 4 + -6 = -2 to get :

2x2 x10⁻² = 4 x10⁻²

in problem 2 you have two tens (similar bases) with powers of 2, and -3 in the denominator, which becomes -(-3) or +3 when it goes to the numerator so add powers of ten 2+3 = 5 to get :

4/2 x10⁵ = 2 x10⁵

In addition and subtraction: first find common factors to change the problem to miltiplication or division so you can use the rules above.

3) (6 x 10^12)+(5 x 10^11) =

10^11 (6x10 + 5) = 65 x 10^11 = 6.5 x 10^12

4) (4 x 10^15)-(2 x 10^13)

10^13 (4 x 10^2 - 2)= 398 x 10^13 = 3.98 x 10^15

Answer 2

(2 x 10^4)times(2 x 10^-6)
= 2*2*10^(4-6)
= 4 * 10^-2
=.04

(4 x 10^2)/(2 x 10^-3)
=4*2*10^(2-3)
=8*10^-1
=.8

(6 x 10^12)+(5 x 10^11)
=6*10^12 + .5*10^12
=6.5 * 10^12

(4 x 10^15)-(2 x 10^13)
= 400 * 10^13 -2*10^13
= 398 * 10^13
=3.98*10^15