It depends. However, when most states calculate your nonresident income tax, they factor in all of your income.
So, in your example, suppose Arkansas would assess 5,000 of tax on $100,000 of income. Since your income is 5% of that amount, your AR tax would be 5% of $5,000, or $250. (Ficticious tax number. Arkansas' tax rate may be higher or lower).
If you live in a state with income tax, your resident state also taxes that income. But they will give you a credit for the tax you must pay to AR on that income so that you are not double-taxed.
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