Question

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

Answer 1

Answer:

Not necessarily

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: $6\cdot 10^7$