If (7.6 x 10^n)(3.5 x 10^3) = 2.66 x 10^9, what is the value of n?

Question

If (7.6 x 10ⁿ)(3.5 x 10³) = 2.66 x 10⁹, what is the value of n?

Answer 1

(7.6 x 10^n)(3.5 x 10^3) = 2.66 x 10^9

step 1] simplify all areas that do not have n

(7.6 x 10^n)(3500) = 260000000

step 2] divide both sides by 3500

7.6 x 10^n = 760000

step 3] divide both sides by 7.6

10^n = 100000

step 4] determine what n is

10^5 = 100000

Answer 2

n is 5

With a calculator set in SCI for scientific notation, just divide 2.66 x 10⁹ by 3.5 x 10³

You can check that by simply doing the multiplication

3.5 x 10³ (7.6 x 10⁵)

While it may appear obvious that 10³ (10⁶) gives 10⁹ . 3.5(7.6) is 26.6

Give it a try.