Dividing Exponents with the Same Base | Exponent Rules | Math with Mr. J

00:06:41
https://www.youtube.com/watch?v=Ei817TVioBU

Zusammenfassung

TLDRIn this video, Mr. J explains how to divide exponents with the same base by keeping the base constant and subtracting the exponents. Through three examples (x^5/x^3, 4^7/4^2, and 2^3/2^8), the concepts are illustrated, demonstrating both straightforward exponents and those with negative results. The final answers are derived clearly, emphasizing the importance of understanding the process behind dividing exponents.

Mitbringsel

  • 📚 Keep the base the same when dividing exponents.
  • ➖ Subtract the exponents from each other.
  • ✨ x^5 divided by x^3 equals x^2.
  • 🍀 4^7 divided by 4^2 equals 4^5 (1024).
  • 🔄 Negative exponent means take the reciprocal: e.g., 2^-5 equals 1/2^5.
  • 🔍 Breaking down the terms helps visualize cancellation.
  • 💡 2^3 divided by 2^8 yields 1/32.
  • 🧮 Understanding these operations strengthens algebra skills.
  • 📏 Practice with various bases to master the concept.
  • 👍 This method is fundamental in simplifying expressions.

Zeitleiste

  • 00:00:00 - 00:06:41

    In this video, Mr. J explains how to divide exponents with the same base by keeping the base the same and subtracting the exponents. He provides examples starting with x^5 divided by x^3, demonstrating that this simplifies to x^(5-3) or x^2 through cancellation of common bases. He repeats this process with 4^7 divided by 4^2, showing that it equals 4^(7-2) or 4^5, resulting in the final answer of 1024. Lastly, he covers the case of 2^3 divided by 2^8, leading to 2^(3-8) or 2^(-5), explaining how negative exponents indicate the reciprocal, yielding 1/2^5 or 1/32. The video concludes with a recap of the method of keeping the base constant and subtracting the exponents.

Mind Map

Video-Fragen und Antworten

  • What is the rule for dividing exponents with the same base?

    Keep the base the same and subtract the exponents.

  • What is x^5 divided by x^3?

    x^5 divided by x^3 equals x^2.

  • How do you handle negative exponents?

    For negative exponents, take the reciprocal.

  • What is 4^7 divided by 4^2?

    4^7 divided by 4^2 equals 4^5, which is 1024.

  • What is 2^3 divided by 2^8?

    2^3 divided by 2^8 equals 2^-5 or 1/32.

Weitere Video-Zusammenfassungen anzeigen

Erhalten Sie sofortigen Zugang zu kostenlosen YouTube-Videozusammenfassungen, die von AI unterstützt werden!
Untertitel
en
Automatisches Blättern:
  • 00:00:00
    [Music]
  • 00:00:00
    welcome to math with mr j
  • 00:00:03
    [Music]
  • 00:00:05
    in this video i'm going to cover how to
  • 00:00:07
    divide exponents with the same base
  • 00:00:10
    for these we keep the base the same and
  • 00:00:13
    then subtract the exponents for example
  • 00:00:17
    if we have x to the power of a divided
  • 00:00:20
    by x to the power of b
  • 00:00:22
    that equals x to the power of a minus b
  • 00:00:27
    let's jump into our examples and see
  • 00:00:30
    exactly how this works starting with
  • 00:00:33
    number 1 where we have x to the power of
  • 00:00:36
    5 divided by x to the power of 3 so we
  • 00:00:40
    keep our base of x the same
  • 00:00:43
    let's write out
  • 00:00:44
    our base of x and then we subtract the
  • 00:00:47
    exponents so 5 minus 3 that gives us an
  • 00:00:52
    exponent of 2. so our solution is x
  • 00:00:56
    squared or x to the power of 2.
  • 00:00:59
    let's break that down and see exactly
  • 00:01:02
    how it works so let's start with x to
  • 00:01:05
    the power of 5 that means
  • 00:01:08
    x
  • 00:01:09
    times x
  • 00:01:11
    times x
  • 00:01:13
    times x
  • 00:01:15
    times x
  • 00:01:16
    and we are dividing it by
  • 00:01:19
    x to the power of 3 or x cubed
  • 00:01:22
    that means x
  • 00:01:24
    times x
  • 00:01:26
    times x
  • 00:01:28
    so once we have this we can cancel out
  • 00:01:31
    x's so to speak because x divided by x
  • 00:01:35
    equals one so these x's can cancel out
  • 00:01:40
    these x's can cancel out and then these
  • 00:01:43
    x's can cancel out
  • 00:01:45
    we don't have any x's left below we can
  • 00:01:49
    think of that as 1 because again x
  • 00:01:52
    divided by x equals 1. so
  • 00:01:55
    i can put a 1 down here and we're left
  • 00:01:58
    with
  • 00:01:59
    2
  • 00:02:00
    x's x times x which equals x squared
  • 00:02:04
    and like i said we have a 1 down here
  • 00:02:07
    which just means
  • 00:02:09
    x squared
  • 00:02:10
    and that gives us the same thing we got
  • 00:02:13
    when we kept the base the same and then
  • 00:02:16
    subtracted the exponents
  • 00:02:19
    let's move on to number 2 where we have
  • 00:02:21
    4 to the power of 7 divided by 4 squared
  • 00:02:26
    keep the base of 4 the same
  • 00:02:29
    so the base of 4 here and then subtract
  • 00:02:33
    the exponents so 7 minus 2
  • 00:02:36
    that gives us an exponent of 5. so 4 to
  • 00:02:40
    the power of 5 and that equals
  • 00:02:44
    1024
  • 00:02:47
    so that's our final solution there
  • 00:02:49
    for number two
  • 00:02:52
    let's break it down and see exactly how
  • 00:02:55
    we got four to the fifth power so four
  • 00:02:58
    to the seventh power we know is four
  • 00:03:01
    times four
  • 00:03:03
    times 4
  • 00:03:04
    times 4
  • 00:03:06
    times 4 times 4
  • 00:03:08
    and finally times 4 and that's divided
  • 00:03:12
    by
  • 00:03:13
    4 squared so 4 times 4 and we can cancel
  • 00:03:17
    out fours 4 divided by 4 equals 1. so
  • 00:03:21
    we'll cancel these fours out and then
  • 00:03:24
    these fours we're left with a 1 down
  • 00:03:28
    below and then we have
  • 00:03:31
    five fours up here
  • 00:03:34
    which that is four
  • 00:03:36
    to the fifth power
  • 00:03:39
    over one which is just
  • 00:03:42
    four
  • 00:03:43
    to the fifth power and that matches our
  • 00:03:46
    answer when we kept the base the same
  • 00:03:49
    and then subtracted the exponents
  • 00:03:52
    and lastly let's move on to number three
  • 00:03:54
    where we have two cubed divided by two
  • 00:03:58
    to the power of 8. so keep the base the
  • 00:04:01
    same so we keep our base of 2
  • 00:04:05
    and then we subtract the exponents so we
  • 00:04:08
    have 3 minus 8. that's actually going to
  • 00:04:12
    give us a negative
  • 00:04:14
    5 so we have 2 to the power of negative
  • 00:04:18
    5. now a negative exponent indicates
  • 00:04:22
    that we're going to perform the inverse
  • 00:04:25
    so when we have a negative exponent we
  • 00:04:28
    take the reciprocal so this is going to
  • 00:04:30
    give us 1
  • 00:04:32
    over
  • 00:04:34
    2 to the power of 5.
  • 00:04:36
    now 2 to the power of 5 equals 32
  • 00:04:39
    so our solution is going to be
  • 00:04:42
    1 32nd or 1 over 32.
  • 00:04:47
    let's break this down and see exactly
  • 00:04:50
    how we ended up with 2 to the power of
  • 00:04:53
    negative 5. so we have 2 cubed which
  • 00:04:56
    means 2
  • 00:04:58
    times 2 times 2
  • 00:05:00
    and then we have 2 to the power of 8 so
  • 00:05:03
    2
  • 00:05:04
    times 2
  • 00:05:06
    times 2
  • 00:05:07
    times 2
  • 00:05:08
    times 2 times 2
  • 00:05:11
    times 2
  • 00:05:12
    and times 2. let's extend
  • 00:05:15
    this line here
  • 00:05:17
    and then we can cancel twos so cancel
  • 00:05:21
    this 2
  • 00:05:22
    and that 2. these two's here and then
  • 00:05:26
    these twos
  • 00:05:28
    so we are left with one up top here
  • 00:05:31
    because remember canceling out those
  • 00:05:34
    twos two divided by two equals one so we
  • 00:05:37
    do have 1 for our numerator here within
  • 00:05:41
    our division problem of 2 cubed divided
  • 00:05:44
    by 2 to the power of 8 and then we are
  • 00:05:47
    left with
  • 00:05:48
    5 2s down here which equals 2 to the
  • 00:05:52
    power of 5. so we have 1
  • 00:05:55
    over 2 to the power of 5
  • 00:05:58
    and we know that 2 to the power of 5
  • 00:06:00
    equals 32
  • 00:06:02
    so we get 1 32nd or 1 over 32 which
  • 00:06:07
    matches
  • 00:06:09
    when we kept the base the same and
  • 00:06:12
    subtracted the exponents
  • 00:06:14
    so there you have it there's how you
  • 00:06:16
    divide exponents with the same base keep
  • 00:06:20
    the base the same and then subtract the
  • 00:06:23
    exponents
  • 00:06:24
    i hope that helped
  • 00:06:26
    thanks so much for watching
  • 00:06:28
    until next time
  • 00:06:30
    peace
  • 00:06:40
    you
Tags
  • exponents
  • division
  • mathematics
  • tutorial
  • negative exponents
  • base
  • calculation
  • reciprocal
  • subtracting exponents
  • power