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

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

Resumen

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.

Para llevar

  • 📚 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.

Cronología

  • 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.

Mapa mental

Vídeo de preguntas y respuestas

  • 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.

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Desplazamiento automático:
  • 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
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    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
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    let's write out
  • 00:00:44
    our base of x and then we subtract the
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    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.
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    let's break that down and see exactly
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    how it works so let's start with x to
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    the power of 5 that means
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    x
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    times x
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    times x
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    times x
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    times x
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    and we are dividing it by
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    x to the power of 3 or x cubed
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    that means x
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    times x
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    times x
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    so once we have this we can cancel out
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    x's so to speak because x divided by x
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    equals one so these x's can cancel out
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    these x's can cancel out and then these
  • 00:01:43
    x's can cancel out
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    we don't have any x's left below we can
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    think of that as 1 because again x
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    divided by x equals 1. so
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    i can put a 1 down here and we're left
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    with
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    2
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    x's x times x which equals x squared
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    and like i said we have a 1 down here
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    which just means
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    x squared
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    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
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    let's move on to number 2 where we have
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    4 to the power of 7 divided by 4 squared
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    keep the base of 4 the same
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    so the base of 4 here and then subtract
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    the exponents so 7 minus 2
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    that gives us an exponent of 5. so 4 to
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    the power of 5 and that equals
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    1024
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    so that's our final solution there
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    for number two
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    let's break it down and see exactly how
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    we got four to the fifth power so four
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    to the seventh power we know is four
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    times four
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    times 4
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    times 4
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    times 4 times 4
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    and finally times 4 and that's divided
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    by
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    4 squared so 4 times 4 and we can cancel
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    out fours 4 divided by 4 equals 1. so
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    we'll cancel these fours out and then
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    these fours we're left with a 1 down
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    below and then we have
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    five fours up here
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    which that is four
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    to the fifth power
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    over one which is just
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    four
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    to the fifth power and that matches our
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    answer when we kept the base the same
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    and then subtracted the exponents
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    and lastly let's move on to number three
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    where we have two cubed divided by two
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    to the power of 8. so keep the base the
  • 00:04:01
    same so we keep our base of 2
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    and then we subtract the exponents so we
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    have 3 minus 8. that's actually going to
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    give us a negative
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    5 so we have 2 to the power of negative
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    5. now a negative exponent indicates
  • 00:04:22
    that we're going to perform the inverse
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    so when we have a negative exponent we
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    take the reciprocal so this is going to
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    give us 1
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    over
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    2 to the power of 5.
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    now 2 to the power of 5 equals 32
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    so our solution is going to be
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    1 32nd or 1 over 32.
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    let's break this down and see exactly
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    how we ended up with 2 to the power of
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    negative 5. so we have 2 cubed which
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    means 2
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    times 2 times 2
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    and then we have 2 to the power of 8 so
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    2
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    times 2
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    times 2
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    times 2
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    times 2 times 2
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    times 2
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    and times 2. let's extend
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    this line here
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    and then we can cancel twos so cancel
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    this 2
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    and that 2. these two's here and then
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    these twos
  • 00:05:28
    so we are left with one up top here
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    because remember canceling out those
  • 00:05:34
    twos two divided by two equals one so we
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    do have 1 for our numerator here within
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    our division problem of 2 cubed divided
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    by 2 to the power of 8 and then we are
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    left with
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    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
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    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
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    matches
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    when we kept the base the same and
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    subtracted the exponents
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    so there you have it there's how you
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    divide exponents with the same base keep
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    the base the same and then subtract the
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    exponents
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    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
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