In the USA, it is possible for an LLC to buy wholesale without paying sales tax and resell the items (including exporting). To do this, you will need to apply for a Reseller Permit, which is free and requires you to fill out a form declaring your intent to resell wholesale items each year.
It is important that you declare the wholesale items and sales of goods on your tax return and are transparent about the overhead costs, the markup and the profit. Stores can (and will) require you to show your Reseller Permit prior to selling goods for resell purposes, especially if they are tax exempt. However, many wholesalers will happily provide you with discounted products void of sales tax once you show your valid permit.
As far as I know, reseller permits expire each year and must be renewed by the Department of Revenue website for your state. Each state's rules may vary on this. Although you can purchase items for resell tax-free, you must charge sales tax on the final product and you also must pay taxes on all profits and sales you make.
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(Disclaimer: This answer is for informational purposes only and does not constitute financial, legal or other professional advice. Use at your own risk, we will not be held liable for the accuracy or use of this information. When in doubt, consult a licensed accountant for specific tax advice).