Find the simplified form of each expression. Give your answer in scientific notation.

(5 x 10^-7) (8 x 10^-4)

A) 4 x 10^13

B) 4 x 10^-12

C) 40 x 10^-10

D) 4 x 10^-10

Answer:D) 4 x 10^-10

Step-by-step explanation:

The given expression is

(5 x 10^-7) (8 x 10^-4)

Firstly, we would multiply the numbers on the left hand side of the 10. It becomes 5 * 8 = 40

Multiplying the 10's, we would apply the law of indices to the powers of 10. It is expressed as

a^2 * a^3 = a^ (2 + 3) = a^6

Therefore,

10^-7 * 10^-4 = 10^ ( - 7 - 4) = 10^ - 11

The simplified form of each expression in scientific notation would be

40 * 10^ - 11

= 4 * 10^ - 11 + 1

= 4 * 10^ - 10