Question

Do exponents need to be the same when multiplying in scientific notation?

Answer 1

Not necessarily

Step-by-step explanation:

The answer would be: not necessarily, there is no such requirement.

Whenever we're multiplying in scientific notation, we may simply multiply the numbers separately and the rest separately. Let's say that in a general case we have two numbers:

`n_1 = a \cdot 10^b`

`n_2 = c \cdot 10^d`

In order to multiply them, we:

• multiply the numbers a and c firstly;
• multiply the 10s now applying the rule
  `10^b\cdot 10^d = 10^(b + d)`;
• multiply result from the step 1 by the result in step 2.

Let's apply this for some specific example, say, we have:

`n_1 = 2\cdot 10^3`

`n_2 = 3\cdot 10^4`

• multiplying 2 and 3:
  `2\cdot 3 = 6`;
• multiplying the 10s:
  `10^3\cdot 10^4 = 10^(3 + 4) = 10^7`;
• multiplying the two results:
  `6\cdot 10^7`