# 冪

| 冪 | U+51AA, &#20906; CJK UNIFIED IDEOGRAPH-51AA |
| ← 冩 [U+51A9] | CJK Unified Ideographs | 冫 → [U+51AB] |

## Translingual
### Han character

冪 (Kangxi radical 14, 冖+14, 16 strokes, cangjie input 月廿日月 (BTAB), four-corner 3722$_7$, composition ⿱冖幕)

#### References

* Kangxi Dictionary: page 131, character 9
* Dai Kanwa Jiten: character 1601
* Dae Jaweon: page 294, character 5
* Hanyu Da Zidian (first edition): volume 1, page 306, character 5
* Unihan data for U+51AA

## Chinese
### Glyph origin

| | Old Chinese |
| 冟 | *hmjeɡ |
| 冖 | *meːɡ |
| 冪 | *meːɡ |
| 羃 | *meːɡ |
| 濗 | *meːɡ |
| 鼏 | *meːɡ |
Originally written as 幎: Phono-semantic compound (形聲／形声, OC *meːɡ) : semantic 巾 (“cloth”) + phonetic 冥 (OC *meːŋ); Xu Shen indicates that the character 幎 means "幔", "tent" (today written as 帷幕).
Later the 六 was corrupted to 大 and the radical was written under the character, thus it became 幂.
艹 was added to form a new phono-semantic compound (形聲／形声, OC *meːɡ) : semantic 巾 (“cloth”) + phonetic 幕 (OC *maːɡ).

### Pronunciation

* Mandarin
    (Pinyin): mì (mi$^4$)
    (Zhuyin): ㄇㄧˋ
* Cantonese (Jyutping): mik$^6$
* Mandarin
** (Standard Chinese)
*** Hanyu Pinyin: mì
*** Zhuyin: ㄇㄧˋ
*** Tongyong Pinyin: mì
*** Wade–Giles: mi$^4$
*** Yale: mì
*** Gwoyeu Romatzyh: mih
*** Palladius: ми (mi)
*** Sinological IPA : /mi⁵¹/
* Cantonese
** (Standard Cantonese, Guangzhou–Hong Kong)
*** Jyutping: mik$^6$
*** Yale: mihk
*** Cantonese Pinyin: mik$^9$
*** Guangdong Romanization: mig$^6$
*** Sinological IPA : /mɪk̚²/
* Middle Chinese: mek
Rime :
| Character | 冪 |
| Reading # | 1/1 |
| Initial (聲) | 明 (4) |
| Final (韻) | 錫 (127) |
| Tone (調) | Checked (Ø) |
| Openness (開合) | Open |
| Division (等) | IV |
| Fanqie | 莫狄切 |
| Baxter | mek |
| Reconstructions ||
| Zhengzhang Shangfang | /mek̚/ |
| Pan Wuyun | /mek̚/ |
| Shao Rongfen | /mɛk̚/ |
| Edwin Pulleyblank | /mɛjk̚/ |
| Li Rong | /mek̚/ |
| Wang Li | /miek̚/ |
| Bernard Karlgren | /miek̚/ |
| Expected Mandarin Reflex | mì |
| Expected Cantonese Reflex | mik$^6$ |
* Old Chinese
    (Baxter–Sagart): /*mˤ[e]k/
    (Zhengzhang): /*meːɡ/
Baxter–Sagart system 1.1 (2014) :
| Character | 冪 |
| Reading # | 1/1 |
| Modern Beijing (Pinyin) | mì |
| Middle Chinese | ‹ mek › |
| Old Chinese | /*mˁ[e]k/ |
| English | cover |
| Notes for Old Chinese notations in the Baxter–Sagart system: * Parentheses "" indicate uncertain presence; * Square brackets "" indicate uncertain identity, e.g. *[t] as coda may in fact be *-t or *-p; * Angle brackets "<>" indicate infix; * Hyphen "-" indicates morpheme boundary; * Period "." indicates syllable boundary. ||
Zhengzhang system (2003) :
| Character | 冪 |
| Reading # | 1/1 |
| No. | 9020 |
| Phonetic component | 冖 |
| Rime group | 錫 |
| Rime subdivision | 0 |
| Corresponding MC rime | 覓 |
| Old Chinese | /*meːɡ/ |
| Notes | 同冖見禮記 |

### Definitions

冪
* to cover with cloth
* cloth cover
* (mathematics) power

### Compounds

* 三次冪／三次幂
* 乘冪／乘幂 (chéngmì)
* 冪冪／幂幂
* 冪函數／幂函数 (mìhánshù)
* 冪定律／幂定律
* 冪律／幂律
* 冪等／幂等
* 冪級數／幂级数
* 冪䍦／幂䍠
* 冪零／幂零
* 升冪 (shēngmì)
* 升冪級數／升幂级数
* 圓冪／圆幂
* 降冪／降幂 (jiàngmì)
* 降冪排列／降幂排列
* 雲冪／云幂

## Japanese
### Kanji

(Hyōgai kanji)

#### Readings

* Go-on: みゃく (myaku)
* Kan-on: べき (beki)
* Kun: おおい (ōi)、ふきん (fukin)

### Etymology

* Kanji in this term
* 冪
* べき Hyōgai
* on'yomi
* This etymology is missing or incomplete. Please add to it, or discuss it at the Etymology scriptorium. Particularly: “「冪」の字義は「覆う、覆うもの」である。江戸時代の和算家は冪の略字として「巾」を用いていた。第二次世界大戦後の漢字制限政策のもと、これらの字は常用漢字・当用漢字に含まれず、1950年代以降の学習参考書などの出版物では仮名書きまたは「累乗」への書き換えが進められ、結果として初等数学の教科書ではもっぱら「累乗」が用いられた。「累乗」の字義は「重ね掛けた乗算」であり、自然数乗以外の冪に対して用いることは字義からすればあまり自然でない。”

### Pronunciation

* (Tokyo) べき [béꜜkì] (Atamadaka –)
* IPA: [be̞kʲi]

### Noun

冪(べき) • (beki)
* (mathematics) a power

#### Synonyms

* 冪乗(べきじょう) (bekijō)

### References

* ↑ Matsumura, Akira, editor (2006), 大辞林 [Daijirin] (in Japanese), Third edition, Tokyo: Sanseidō, →ISBN

## Korean
### Hanja

冪 • (myeok) (hangeul 멱, revised myeok, McCune–Reischauer myŏk)
* This term needs a translation to English. Please help out and add a translation, then remove the text {{rfdef}}.

## Vietnamese
### Han character

冪: Hán Việt readings: mịch, mạc
* conceal; cloak.