Correct spelling, explanation: smooths is a verb whose infinitive form is to smooth. When an -s letter is added to it, it is the third singular form of the present simple tense. Smooths probably comes from an Old English form smoth, but it wasn’t until the Middle Ages when smooths started to look the way we know it today. In modern English smooths is a commonly used verb.

Definition of smooths:
1. verb (present simple 3rd person singular) – to make some surface flat; to rub a substance e.g. into your skin; to make some problems go away.
Every time there is some stressful situation, she nervously smooths down her hair.
Her skin is so soft because after every bath she smooths some lotion into all the dry skin patches.
She’s a professional and smooths all the problems away with a few simple tricks in our computer system.

Expressions and collocations with smooths:
A few commonly used collocations and expressions with smooths are: smooths carefully, smooths gently, and smooths down.
After every walk, she smooths the fur of her dog carefully to check if there are any ticks.
Every mother smooths her baby’s hair gently as it’s the most basic sign of unconditioned love.
My mother always smooths my hair back, which I really can’t stand.

Incorrect spelling, explanation: the base form of the verb smooths is smooth and when a verb ends with an -h, we simply add an -s letter to it when we form the third singular form of the present simple tense. Therefore, the only correct spelling is smooths. Nevertheless, some English users think that we add an -es ending as it happens in case of verbs ending with -ch and they misspell the word as smoothes, which is wrong.