Hello. In this math educational post, I go over working with negative exponents. Rendered math text is from the use of QuickLaTeX.com <center><img src="https://cdn.pixabay.com/photo/2016/08/26/15/20/mathematics-1622448_960_720.jpg" /></center> <center><a href="https://cdn.pixabay.com/photo/2016/08/26/15/20/mathematics-1622448_960_720.jpg">Pixabay Image Source</a></center> ## Topics --- * Exponents Review * Dealing With Negative Exponents * Practice Problems * Answers To Practice Problems ## Exponents Review --- An exponent can be viewed as a number counter of how many times a number is multiplied by itself. Instead of writing 2 x 2 x 2 x 2 x 2, we can write https://quicklatex.com/cache3/ed/ql_b743a7a19ccbf511aba5d3dc565942ed_l3.png where the base 2 is the number being multiplied by itself. The exponent 5 represents how many times the two is used when multiplying by itself. When it comes to fractional exponents it is kind of difficult to explain what it is. Having https://quicklatex.com/cache3/f4/ql_ec930800d1e902aafa1a6b05db2b36f4_l3.png is actually taking the square root of 2. When it comes to https://quicklatex.com/cache3/e6/ql_63249a44309c53b032bb55db1b491ee6_l3.png, this is taking the fifth root of 7. Consider the case where the exponent does not have a numerator of one such as https://quicklatex.com/cache3/35/ql_f5d93f3f318255c4622d8c2360218635_l3.png. With https://quicklatex.com/cache3/35/ql_f5d93f3f318255c4622d8c2360218635_l3.png I do ten squared to obtain 100 and then take the third root of 100. With a non-zero base and an exponent zero the number results in a 1. Examples include https://quicklatex.com/cache3/10/ql_1394f90b41784e6aa1cd2ea4b57e2b10_l3.png in which they equal one. <center><img src="https://cdn.pixabay.com/photo/2020/08/03/05/03/students-5459157_960_720.jpg" /></center> <center><a href="https://cdn.pixabay.com/photo/2020/08/03/05/03/students-5459157_960_720.jpg">Pixabay Image Source</a></center> ## Dealing With Negative Exponents --- Negative exponents operate differently than positive exponents. It is common math practice to convert negative exponent values into its equivalent value with positive exponents. Given https://quicklatex.com/cache3/40/ql_f19ae5d87903b040c29110a52a5e2840_l3.png this turns into its reciprocal of 1 divided by x: <center>https://quicklatex.com/cache3/40/ql_173839164bb590969a9bc54809056e40_l3.png</center> The more confusing variation of the above is dealing with https://quicklatex.com/cache3/23/ql_6c1cc17da6201bc59e67fe8dc9bf0f23_l3.png which ends up being x. <center>https://quicklatex.com/cache3/f8/ql_dc594655fb9f04fac6d1d6334e9caef8_l3.png</center> **Example One** Evaluate https://quicklatex.com/cache3/1f/ql_7d0c51b15e1c7087a564ec1817ea051f_l3.png. **Solution** <center>https://quicklatex.com/cache3/1d/ql_b9234e31c1173a356c582d367bc0721d_l3.png</center> **Example Two** Evaluate one tenth to the power of negative 2. <center>https://quicklatex.com/cache3/49/ql_999c17f1c991ad7a3336c4d945499a49_l3.png</center> **Example Three** Convert the following expression into positive exponents. <center>https://quicklatex.com/cache3/9b/ql_a9bd4b5a4edf27ac86fdc45c8a4cc89b_l3.png</center> **Solution** <center>https://quicklatex.com/cache3/77/ql_aae990cd5f4e0ace6da05878bfa02677_l3.png</center> With this case, you can "flip" the fraction and remove the negative signs from the exponents. <center><img src="https://cdn.pixabay.com/photo/2013/05/16/09/05/mathematics-111423_960_720.jpg" /></center> <center><a href="https://cdn.pixabay.com/photo/2013/05/16/09/05/mathematics-111423_960_720.jpg">Pixabay Image Source</a></center> ## Practice Problems --- Evaluate the following into a single number. 1) https://quicklatex.com/cache3/1f/ql_7d0c51b15e1c7087a564ec1817ea051f_l3.png 2) https://quicklatex.com/cache3/76/ql_c2948cfcb1a5dac884e01b355af51776_l3.png 3) https://quicklatex.com/cache3/e1/ql_1e12a6c385076ada25da4f1c9693b6e1_l3.png 4) https://quicklatex.com/cache3/ec/ql_8b19a11878541948a99d2f62f70e24ec_l3.png Convert into positive exponents. 5) https://quicklatex.com/cache3/02/ql_938e121c89001a3e178a9f766c628802_l3.png 6) https://quicklatex.com/cache3/62/ql_8b3c6be3b430163addd5b69088bec562_l3.png 7) https://quicklatex.com/cache3/2b/ql_fd31e13455d68ced2a11382c07a58b2b_l3.png 8) https://quicklatex.com/cache3/c6/ql_3de18c00711f50992bcb8f49c245b9c6_l3.png ## Answers To Practice Problems --- 1) 1/8 2) 1/9 3) 1/4 4) 49/4 --- Convert into positive exponents. 1) https://quicklatex.com/cache3/87/ql_b4349f6aa682c50f27b4d142a0834b87_l3.png 2) https://quicklatex.com/cache3/f5/ql_9337ef8c0c4356c8ea9c8b8df36b6bf5_l3.png 3) https://quicklatex.com/cache3/0b/ql_31576f7a1967b53395d190fdc5feb80b_l3.png 4) https://quicklatex.com/cache3/c5/ql_4d20ba16c66e033f2f38c0057bce09c5_l3.png <center><img src="https://cdn.pixabay.com/photo/2015/11/15/07/43/mathematics-1044075_960_720.jpg" /></center> <center><a href="https://cdn.pixabay.com/photo/2015/11/15/07/43/mathematics-1044075_960_720.jpg">Pixabay Image Source</a></center> --- <center>Thank you for reading.</center>
author | dkmathstats |
---|---|
permlink | negative-exponents |
category | hive-122481 |
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last_update | 2020-08-17 00:36:51 |
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tombstone | 0 | 19,145,703,546 | 0.9% | ||
onealfa | 0 | 8,492,098,212 | 0.44% | ||
gerber | 0 | 137,843,224,113 | 2% | ||
ezzy | 0 | 154,034,061,424 | 2% | ||
fiveboringgames | 0 | 447,191,557,274 | 100% | ||
exyle | 0 | 152,836,069,663 | 2% | ||
netaterra | 0 | 40,516,353,158 | 1.8% | ||
someguy123 | 0 | 89,954,064,888 | 3% | ||
bestofreddit | 0 | 1,182,078,935 | 100% | ||
zorg67 | 0 | 533,557,603 | 100% | ||
privex | 0 | 3,688,744,849 | 4% | ||
dune69 | 0 | 9,122,414,472 | 2% | ||
roomservice | 0 | 100,743,197,342 | 2.25% | ||
mys | 0 | 315,926,571 | 0.2% | ||
shitsignals | 0 | 786,291,962 | 2% | ||
themarkymark | 0 | 2,359,202,573,673 | 12% | ||
felander | 0 | 10,217,538,199 | 2% | ||
accelerator | 0 | 56,012,679,369 | 5% | ||
buildawhale | 0 | 8,273,781,682,686 | 12% | ||
yogacoach | 0 | 877,203,986 | 1% | ||
therealwolf | 0 | 931,999,874,203 | 3% | ||
deathwing | 0 | 2,696,598,245 | 2% | ||
makerhacks | 0 | 30,697,537,580 | 12% | ||
kevinbacon | 0 | 1,042,675,268 | 100% | ||
caladan | 0 | 6,879,974,039 | 2% | ||
coyotelation | 0 | 2,262,322,459 | 10% | ||
emrebeyler | 0 | 33,119,986,988 | 2% | ||
smartsteem | 0 | 195,540,304,209 | 3% | ||
nealmcspadden | 0 | 25,396,865,874 | 2% | ||
purefood | 0 | 28,158,026,344 | 2% | ||
tobias-g | 0 | 11,110,153,081 | 9% | ||
amico | 0 | 15,796,456,536 | 1% | ||
bestboom | 0 | 8,250,191,869 | 2% | ||
freddio | 0 | 19,472,454,014 | 15% | ||
gadrian | 0 | 55,121,821,670 | 35% | ||
tonimontana | 0 | 282,263,379 | 11.21% | ||
themightyvolcano | 0 | 3,079,196,006 | 2% | ||
steem.services | 0 | 224,195,559,172 | 2% | ||
enforcer48 | 0 | 116,794,655,922 | 15% | ||
swisswitness | 0 | 1,158,949,422 | 2% | ||
we-are-lucky | 0 | 13,335,150,910 | 84.08% | ||
dalz | 0 | 2,820,760,839 | 1% | ||
zuerich | 0 | 276,375,150,027 | 6% | ||
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dlike | 0 | 24,467,638,137 | 2% | ||
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gordonramzy | 0 | 606,586,134 | 100% | ||
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bobby.madagascar | 0 | 1,914,935,566 | 1.5% | ||
oakshieldholding | 0 | 107,322,477 | 100% | ||
laissez-faire | 0 | 76,778,077 | 100% | ||
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creativeblue | 0 | 5,925,619,725 | 50% | ||
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aqua.nano | 0 | 6,464,363,526 | 100% | ||
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limka | 0 | 22,764,136 | 10% | ||
samuel.steem | 0 | 982,758,917 | 100% | ||
pedrobrito2004 | 0 | 1,025,159,885 | 3% | ||
paolo.senegal | 0 | 1,449,142,865 | 100% | ||
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tinyhousecryptos | 0 | 531,601,791 | 5% | ||
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maruskina | 0 | 31,659,326,009 | 50% | ||
firefuture | 0 | 595,078,319 | 1% | ||
nalacanecorso | 0 | 1,231,034,528 | 100% | ||
milu-the-dog | 0 | 839,403,741 | 2% | ||
triplea.bot | 0 | 673,666,977 | 2% | ||
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asteroids | 0 | 1,966,106,703 | 1.8% | ||
abh12345.stem | 0 | 773,429,242 | 100% | ||
botante | 0 | 4,738,336,257 | 2% | ||
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btc4breackfast | 0 | 1,884,384,789 | 100% | ||
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vxc.stem | 0 | 0 | 11.21% | ||
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huaren.news | 0 | 34,930,925,293 | 70% | ||
cd-stem | 0 | 531,162,388 | 100% | ||
gerbo | 0 | 0 | 2% | ||
pecoshop | 0 | 1,896,271,411 | 100% | ||
stem.curate | 0 | 957,829,189 | 100% | ||
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hivecur | 0 | 50,952,766,339 | 2% | ||
adolfom | 0 | 2,438,963,640 | 100% | ||
chartreader | 0 | 61,554,447 | 2% |