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Eksponen ~ Matematika SMA | Catatan Nurkholis

Eksponen ~ Matematika SMA

Pengertian

Secara umum Eksponen dapat dinyatakan sebagai berikut:$$a^n=atimes atimes atimes cdots times a$$, untuk $n$ bilangan bulat positif.

Contoh

$2^3=2times2times2=8$

Sifat-Sifat Eksponen

Untuk $a,bintextbf{R}$ berlaku:

  1. $a^m.a^n=a^{m+n}$
  2. $frac{a^m}{a^n}=a^{m-n}$
  3. $left(a^mright)^n=a^{mn}$
  4. $displaystylefrac{1}{a^m}=a^{-m}$
  5. $a^{frac{m}{n}}=sqrt[n]{a^m}$
  6. $a^m.b^m=left(abright)^m$
  7. $displaystylefrac{a^m}{b^m}=left(frac{a}{b}right)^m$
  8. $a^0=1,quad ane0$
  9. $1^m=1$

Contoh

Bentuk sederhana dari $displaystylefrac{x^5-x^3}{(x+1)^2}$ adalah ….

Solusi

$begin{aligned}
frac{x^5-x^3}{(x+1)^2}&=frac{x^3(x^2-1)}{(x+1)^2}\
&=frac{x^3(x-1)(x+1)}{(x+1)(x+1)}\
&=frac{x^3(x-1)}{x+1}
end{aligned}$

Latihan Soal

Tentukan Nilai $k$ yang memenuhi $x^a(x^{a+1})^a(x^a)^{1-a}=x^{k-1}$

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