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

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

摘要

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.

心得

  • 📚 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.

时间轴

  • 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.

思维导图

视频问答

  • 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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  • 00:00:00
    [Music]
  • 00:00:00
    welcome to math with mr j
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    [Music]
  • 00:00:05
    in this video i'm going to cover how to
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    divide exponents with the same base
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    for these we keep the base the same and
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    then subtract the exponents for example
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    if we have x to the power of a divided
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    by x to the power of b
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    that equals x to the power of a minus b
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    let's jump into our examples and see
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    exactly how this works starting with
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    number 1 where we have x to the power of
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    5 divided by x to the power of 3 so we
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    keep our base of x the same
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    let's write out
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    our base of x and then we subtract the
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    exponents so 5 minus 3 that gives us an
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    exponent of 2. so our solution is x
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    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
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    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
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    when we kept the base the same and then
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    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
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    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
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    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
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    so we are left with one up top here
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    because remember canceling out those
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    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
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    power of 5. so we have 1
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    over 2 to the power of 5
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    and we know that 2 to the power of 5
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    equals 32
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    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
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    thanks so much for watching
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    until next time
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    peace
  • 00:06:40
    you
标签
  • exponents
  • division
  • mathematics
  • tutorial
  • negative exponents
  • base
  • calculation
  • reciprocal
  • subtracting exponents
  • power