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How do you simplify $(10^{4}) (10^{9})$ $(10^4)(10^9)$ ?

2 Answers

Feb 5, 2016

$(10^{4}) (10^{9}) = 10^{13}$ $(10^4)(10^9) = 10^13$

Explanation:

One way is to remember the general relation:
$XXX b^{p} \times b^{q} = b^{p + q}$ $color(white)("XXX")b^pxxb^q = b^(p+q)$

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

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

George C. · mason m

Feb 5, 2016

$(10^{4}) (10^{9}) = 10^{13}$ $(10^4)(10^9) = 10^13$

Explanation:

If $k$ $k$ 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:

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

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