exponentials

[aditi610]

formula for multiplying exponential expression is a^x a^ y = a^x+y
however, how do I apply that to a problem where the bases are not equal (7 x 10^2) x (4 x 10 ^ 5) Thank you

 

[Deleted member 4993]

formula for multiplying exponential expression is a^x a^ y = a^x+y
however, how do I apply that to a problem where the bases are not equal (7 x 10^2) x (4 x 10 ^ 5) Thank you

In your problem the base of the exponents ARE equal.

\(\displaystyle (7 * 10^2) x (4 * 10^5) \ = \ 7 * 4 * 10^2 * 10^5 \ = \ 28 * 10^{2+5} \ = \ 28 * 10^7 \ = \ 2.8 * 10^8\)............fixed typos

 

[aditi610]

shouldnt it be 7 x 4 x 10^2 x 10^5 = 28 x 10^ 7....but the answer key says 2.8 x 10^ 8?

 

[Deleted member 4993]

shouldnt it be 7 x 4 x 10^2 x 10^5 = 28 x 10^ 7

yes - I misread the question and now fixed it above

....but the answer key says 2.8 x 10^ 8

Yes - that is correct in scientific notation - there we need only unit position.

My answer was related to your confusion regarding the base of the exponent.
?

 

[aditi610]

y is it not 28 x 10^ 7 but 2.8 x 10 ^ 8? can u plz explain that?

 

[Denis]

formula for multiplying exponential expression is a^x a^ y = a^x+y

NO; a^x a^ y = a^(x+y)
What you have means a^x, then add y

 

[Deleted member 4993]

y is it not 28 x 10^ 7 but 2.8 x 10 ^ 8? can u plz explain that?

Numerically:

\(\displaystyle 28 * 10^7 \ = \ 2.8 * 10^8\)

By convention, while writing answer in scientific notation - we would express the answer as 2.8 * 10[sup:2ofme9w5]8[/sup:2ofme9w5]

By convention, while writing answer in engineering notation - we would express the answer as 280 * 10[sup:2ofme9w5]6[/sup:2ofme9w5]

I repeat - those are numerically same - just following different convention of reporting.

 

[mmm4444bot]

y is it not 28 x 10^ 7 but 2.8 x 10 ^ 8

When typing mathematics, please do not use the symbol y to represent the word "why".

I believe that Scientific Notation requires the number in front (I'll call it n) to be in this range:

1 < n < 10

Therefore, you shift the decimal point to make it so, followed by adjusting the exponent to compensate.