Question

How do you simplify `(10^4)(10^9)`?

Answer 1

`(10^4)(10^9) = 10^13`

Explanation:

One way is to remember the general relation:
`color(white)("XXX")b^pxxb^q = b^(p+q)`

Or
`color(white)("XXX")10^4` means `10` multiplied together `4` times
`color(white)("XXX")`and
`color(white)("XXX")10^9` means `10` multiplied together `9` times

`color(white)("XXX")`So `10^4xx10^9` will be `10` multiplied together `13` times
`color(white)("XXX")`which can be written `10^13`

Answer 2

`(10^4)(10^9) = 10^13`

Explanation:

If `k` is a positive integer then:

`10^k = stackrel "k times" overbrace(10xx10xx...xx10)`

So if `a` and `b` are positive integers then we find:

`10^a xx 10^b = stackrel "a times" overbrace(10xx10xx...xx10) xx stackrel "b times" overbrace(10xx10xx...xx10)`

`=stackrel "a + b times" overbrace(10xx10xx...xx10)=10^(a+b)`

In our example, `a=4` and `b=9` and we find:

`(10^4)(10^9) = 10^(4+9) = 10^13`