{"id":2272,"date":"2017-06-15T21:59:56","date_gmt":"2017-06-15T21:59:56","guid":{"rendered":"http:\/\/10.10.10.4:9191\/softlect\/?p=2272"},"modified":"2019-06-22T14:13:17","modified_gmt":"2019-06-22T14:13:17","slug":"exponent-rules","status":"publish","type":"post","link":"http:\/\/softlect.com\/index.php\/exponent-rules\/","title":{"rendered":"Exponent Rules"},"content":{"rendered":"

The base a is raised to the power of n is equal to the multiplication of a, n times:<\/p>\n

an<\/sup><\/em> = a <\/em>\u00d7 a <\/em>\u00d7 … <\/em>\u00d7 a<\/em><\/p>\n

n times<\/p>\n

a is the base and n is the exponent.<\/p>\n

Exponents rules and properties<\/p>\n

\n
\n
Rule name<\/strong><\/div>\n
Rule<\/strong><\/div>\n
Example<\/strong><\/div>\n<\/div>\n
\n
Product rules<\/div>\n
a n<\/sup><\/em> \u00b7 a m<\/sup><\/em> = a n+m<\/sup><\/em><\/div>\n
23<\/sup> \u00b7 24<\/sup> = 23+4<\/sup> = 128<\/div>\n<\/div>\n
\n
 <\/div>\n
a n<\/sup><\/em> \u00b7 b n<\/sup><\/em> = (a <\/em>\u00b7 b<\/em>) n<\/sup><\/em><\/div>\n
32<\/sup> \u00b7 42<\/sup> = (3\u00b74)2<\/sup> = 144<\/div>\n<\/div>\n
\n
Quotient rules<\/div>\n
a n<\/sup><\/em> \/ a m<\/sup><\/em> = a n<\/sup><\/em>–m<\/em><\/sup><\/div>\n
25<\/sup> \/ 23<\/sup> = 25-3<\/sup> = 4<\/div>\n<\/div>\n
\n
 <\/div>\n
a n<\/sup><\/em> \/ b n<\/sup><\/em> = (a <\/em>\/ b<\/em>) n<\/sup><\/em><\/div>\n
43<\/sup> \/ 23<\/sup> = (4\/2)3<\/sup> = 8<\/div>\n<\/div>\n
\n
Power rules<\/div>\n
(bn<\/sup><\/em>)m<\/em><\/sup> = bn\u00b7m<\/sup><\/em><\/div>\n
(23<\/sup>)2<\/sup> = 23\u00b72<\/sup> = 64<\/div>\n<\/div>\n
\n
 <\/div>\n
b<\/sub>n<\/em>m<\/em><\/sup> = b<\/sub>(n<\/em>m<\/em><\/sup>)<\/div>\n
2<\/sub>32<\/sup> = 2<\/sub>(32<\/sup>)= 512<\/sub><\/div>\n<\/div>\n
\n
 <\/div>\n
m<\/em><\/sup>\u221a(bn<\/sup><\/em>) = b<\/em> n<\/em>\/m<\/em><\/sup><\/div>\n
2<\/sup>\u221a(26<\/sup>) = 26\/2<\/sup> = 8<\/div>\n<\/div>\n
\n
 <\/div>\n
b<\/em>1\/n<\/em><\/sup> = n<\/sup><\/em>\u221ab<\/em><\/div>\n
81\/3<\/sup> = 3<\/sup>\u221a8 = 2<\/div>\n<\/div>\n
\n
Negative exponents<\/div>\n
b-n<\/sup><\/em> = 1 \/ bn<\/sup><\/em><\/div>\n
2-3<\/sup> = 1\/23<\/sup> = 0.125<\/div>\n<\/div>\n
\n
Zero rules<\/div>\n
b<\/em>0<\/sup> = 1<\/div>\n
50<\/sup> = 1<\/div>\n<\/div>\n
\n
 <\/div>\n
0n<\/sup><\/em> = 0 , for n<\/em>>0<\/div>\n
05<\/sup> = 0<\/div>\n<\/div>\n
\n
One rules<\/div>\n
b<\/em>1<\/sup> = b<\/em><\/div>\n
51<\/sup> = 5<\/div>\n<\/div>\n
\n
 <\/div>\n
1n<\/sup><\/em> = 1<\/div>\n
15<\/sup> = 1<\/div>\n<\/div>\n
\n
Minus one rule<\/div>\n
\"\"<\/div>\n
(-1)5<\/sup> = -1<\/div>\n<\/div>\n
\n
Derivative rule<\/div>\n
(xn<\/sup><\/em>)‘ <\/em>= n<\/em>\u00b7x n<\/sup><\/em>-1<\/sup><\/div>\n
(x<\/em>3<\/sup>)‘ <\/em>= 3\u00b7x<\/em>3-1<\/sup><\/div>\n<\/div>\n
\n
Integral rule<\/div>\n
\u222b xn<\/sup>dx<\/em> = xn<\/sup><\/em>+1<\/sup>\/(n<\/em>+1)+C<\/em><\/div>\n
\u222b x<\/em>2<\/sup>dx<\/em> = x<\/em>2+1<\/sup>\/(2+1)+C<\/em><\/div>\n<\/div>\n<\/div>\n

Exponents product rules<\/h3>\n

Product rule with same base<\/h4>\n

an<\/sup><\/em> \u00b7 am<\/sup><\/em> = an+m<\/sup><\/em><\/p>\n

Example:<\/p>\n

23<\/sup> \u00b7 24<\/sup> = 23+4<\/sup> = 27<\/sup> = 2\u00b72\u00b72\u00b72\u00b72\u00b72\u00b72 = 128<\/p>\n

Product rule with same exponent<\/h4>\n

an<\/sup><\/em> \u00b7 bn<\/sup><\/em> = (a <\/em>\u00b7 b<\/em>)n<\/sup><\/em><\/p>\n

Example:<\/p>\n

32<\/sup> \u00b7 42<\/sup> = (3\u00b74)2<\/sup> = 122<\/sup> = 12\u00b712 = 144<\/p>\n

Exponents quotient rules<\/h3>\n

Quotient rule with same base<\/h4>\n

an<\/sup><\/em> \/ am<\/sup><\/em> = an<\/sup><\/em>–m<\/em><\/sup><\/p>\n

Example:<\/p>\n

25<\/sup> \/ 23<\/sup> = 25-3<\/sup> = 22<\/sup> = 2\u00b72 = 4<\/p>\n

Quotient rule with same exponent<\/h4>\n

an<\/sup><\/em> \/ bn<\/sup><\/em> = (a <\/em>\/ b<\/em>)n<\/sup><\/em><\/p>\n

Example:<\/p>\n

43<\/sup> \/ 23<\/sup> = (4\/2)3<\/sup> = 23<\/sup> = 2\u00b72\u00b72 = 8<\/p>\n

Exponents power rules<\/h3>\n

Power rule I<\/h4>\n

(an<\/sup><\/em>) m<\/em><\/sup> = a n\u00b7m<\/sup><\/em><\/p>\n

Example:<\/p>\n

(23<\/sup>)2<\/sup> = 23\u00b72<\/sup> = 26<\/sup> = 2\u00b72\u00b72\u00b72\u00b72\u00b72 = 64<\/p>\n

Power rule II<\/h4>\n

a<\/sub>n<\/em>m<\/em><\/sup> = <\/sub>a<\/sub><\/em>(n<\/em>m<\/em><\/sup>)<\/p>\n

Example:<\/p>\n

2<\/sub>32<\/sup> = 2<\/sub>(32<\/sup>) = 2<\/sub>(3\u00b73) = 2<\/sub>9 = 2\u00b72\u00b72\u00b72\u00b72\u00b72\u00b72\u00b72\u00b72 = 512<\/sub><\/p>\n

Power rule with radicals<\/h4>\n

m<\/em><\/sup>\u221a(a n<\/sup><\/em>) = a n<\/sup><\/em>\/m<\/em><\/sup><\/p>\n

Example:<\/p>\n

2<\/sup>\u221a(26<\/sup>) = 26\/2<\/sup> = 23<\/sup> = 2\u00b72\u00b72 = 8<\/p>\n

Negative exponents rule<\/h3>\n

b-n<\/sup><\/em> = 1 \/ bn<\/sup><\/em><\/p>\n

Example:<\/p>\n

2-3<\/sup> = 1\/23<\/sup> = 1\/(2\u00b72\u00b72) = 1\/8 = 0.125<\/p>\n","protected":false},"excerpt":{"rendered":"

The base a is raised to the power of n is equal to the multiplication of a, n times: an = a \u00d7 a \u00d7 … \u00d7 a n times… <\/p>\n","protected":false},"author":1,"featured_media":3129,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[34],"tags":[],"aioseo_notices":[],"amp_enabled":true,"_links":{"self":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/2272"}],"collection":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/comments?post=2272"}],"version-history":[{"count":11,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/2272\/revisions"}],"predecessor-version":[{"id":3545,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/2272\/revisions\/3545"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/media\/3129"}],"wp:attachment":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/media?parent=2272"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/categories?post=2272"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/tags?post=2272"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}