but Allah is omnipotent (can do everything), why didnt he make everyone equal?
2:177 "It is not righteousness that ye turn your faces Towards east or West; but it is righteousness to believe in God and the Last Day, and the Angels, and the Book, and the Messengers; to spend of your substance, out of love for Him, for your kin, for orphans, for the needy, for the wayfarer, for those who ask, and for the ransom of slaves; to be steadfast in prayer, and practice regular charity; to fulfil the contracts which ye have made; and to be firm and patient, in pain (or suffering) and adversity, and throughout all periods of panic. Such are the people of truth, the God-fearing."
2:221 "Do not marry unbelieving women (idolaters), until they believe: A slave woman who believes is better than an unbelieving woman, even though she allures you. Nor marry (your girls) to unbelievers until they believe: A man slave who believes is better than an unbeliever, even though he allures you. Unbelievers do (but) beckon you to the Fire. But God beckons by His Grace to the Garden (of bliss) and forgiveness, and makes His Signs clear to mankind: That they may celebrate His praise."
infact a slave woman here in this verse is better than non beliving women you see how even that she is a slave she is still better??
24:31 "And say to the believing women that they should lower their gaze and guard their modesty; that they should not display their beauty and ornaments except what (must ordinarily) appear thereof; that they should draw their veils over their bosoms and not display their beauty except to their husbands, their fathers, their husband's fathers, their sons, their husbands' sons, their brothers or their brothers' sons, or their sisters' sons, or their women, or the slaves whom their right hands possess, or male servants free of physical needs, or small children who have no sense of the shame of sex; and that they should not strike their feet in order to draw attention to their hidden ornaments. And O ye Believers! turn ye all together towards God, that ye may attain Bliss."
"When the slave of anyone amongst you prepares food for him and he serves him after having sat close to (and undergoing the hardship of) heat and smoke, he should make him (the slave) sit along with him and make him eat (along with him), and if the food seems to run short, then he should spare some portion for him (from his own share) - (another narrator) Dawud said:" i. e. a morsel or two". 4097.
"At Ar-Rabadha I met Abu Dhar who was wearing a cloak, and his slave, too, was wearing a similar one. I asked about the reason for it. He replied, "I abused a person by calling his mother with bad names." The Prophet said to me, 'O Abu Dhar! Did you abuse him by calling his mother with bad names You still have some characteristics of ignorance. Your slaves are your brothers and Allah has put them under your command. So whoever has a brother under his command should feed him of what he eats and dress him of what he wears. Do not ask them (slaves) to do things beyond their capacity (power) and if you do so, then help them.'
"The Prophet said, 'None of you will have faith till he wishes for his (Muslim) brother [this includes slaves, since a slave is considered a brother as shown above] what he likes for himself.' (Translation of Sahih Bukhari, Belief, Volume 1, Book 2, Number 12)"
"Some people asked Allah's Apostle, 'Whose Islam is the best? i.e. (Who is a very good Muslim)?' He replied, 'One who avoids harming the Muslims with his tongue and hands.' (Translation of Sahih Bukhari, Belief, Volume 1, Book 2, Number 10)"
that include slave muslim
"A man asked the Prophet, 'What sort of deeds or (what qualities of) Islam are good?' The Prophet replied, 'To feed (the poor) and greet those whom you know and those whom you do not Know.' (Translation of Sahih Bukhari, Belief, Volume 1, Book 2, Number 11)"
4:92 "Never should a believer kill a believer; but (If it so happens) by mistake, (Compensation is due): If one (so) kills a believer, it is ordained that he should free a believing slave, and pay compensation to the deceased's family, unless they remit it freely. If the deceased belonged to a people at war with you, and he was a believer, the freeing of a believing slave (Is enough). If he belonged to a people with whom ye have treaty of Mutual alliance, compensation should be paid to his family, and a believing slave be freed. For those who find this beyond their means, (is prescribed) a fast for two months running: by way of repentance to God: for God hath all knowledge and all wisdom."
5:89 "God will not call you to account for what is futile in your oaths, but He will call you to account for your deliberate oaths: for expiation, feed ten indigent persons, on a scale of the average for the food of your families; or clothe them; or give a slave his freedom. If that is beyond your means, fast for three days. That is the expiation for the oaths ye have sworn. But keep to your oaths. Thus doth God make clear to you His signs, that ye may be grateful."
58:3 "But those who divorce their wives by Zihar, then wish to go back on the words they uttered, (It is ordained that such a one) should free a slave before they touch each other: Thus are ye admonished to perform: and God is well-acquainted with (all) that ye do."
"The Prophet said, "Give food to the hungry, pay a visit to the sick and release (set free) the one in captivity (by paying his ransom)." (Translation of Sahih Bukhari, Food, Meals, Volume 7, Book 65, Number 286)"
"'Abdullah b. 'Umar reported that 'Umar b. Khattab asked the Messenger of Allah (may peace be upon him) as he was at ji'rana (a town near Mecca) on his way back from Ta'if: Messenger of Allah, I had taken a vow during the days of Ignorance that I would observe I'tikaf for one day in the Sacred Mosque. So what is your opinion? He said: Go and observe I'tikaf for a day. And Allah's Messenger (may peace be upon him) gave him a slave girl out of the one-fifth (of the spoils of war meant for the Holy Prophet). And when Allah's Messenger (may peace be upon him) set the war prisoners free. 'Umar b. Khattab heard their voice as they were saying: Allah's Messenger (may peace be upon him) has set us free. He (Hadrat 'Umar) said: What is this? They said: Allah's Messenger (may peace be upon him) has set free the prisoners of war (which had fallen to the lot of people). Thereupon he (Hadrat 'Umar) said: Abdullah, go to that slave-girl and set her free. (Sahih Muslim, The Book of Oaths (Kitab Al-Aiman), Book 015, Number 4074)"
"Zadhan reported that Ibn Umar called his slave and he found the marks (of beating) upon his back. He said to him: I have caused you pain. He said: No. But he (Ibn Umar) said: You are free. He then took hold of something from the earth and said: There is no reward for me even to the weight equal to it. I heard Allah's Messenger (may peace be upon him) as saying: He who beats a slave without cognizable offence of his or slaps him, then expiation for it is that he should set him free. (Sahih Muslim, The Book of Oaths (Kitab Al-Aiman), Book 015, Number 4079)"
NOW i can go on and on and there is many to come to put you might ask can a slave ask his master to set him free?

??
the answer is YES
24:33 "Let those who find not the wherewithal for marriage keep themselves chaste, until God gives them means out of His grace. And if any of your slaves ask for a deed in writing
(to enable them to earn their freedom for a certain sum), give them such a deed if ye know any good in them: yea, give them something yourselves out of the means which God has given to you. But force not your maids to prostitution when they desire chastity, in order that ye may make a gain in the goods of this life. But if anyone compels them, yet, after such compulsion, is God, Oft-Forgiving, Most Merciful (to them),"
If you ask is there human Equality in Islam then i think of what i presented here the answer is Yes