# BAB IA Perpangkatan/Eksponen

Perpangkatan/Eksponen:

Pengertian:

$a^{n}~$= a x a x a x …. x a (n faktor)

Sifat-sifat Perpangkatan :

1. $a^{m}.a^{n}= a^{m+n}$
2. $a^{m}:a^{n} = \frac{a^{m}}{a^{n}}= a^{m-n}; a \neq 0$
3. $(a^{m})^{n} = a^{mn}$
4. $(a.b)^{n} = a^{n}.b^{n}$
5. $\left ( \frac{a}{b} \right )^{n}= \frac{a^{n}}{b^{n}}~ ;b\neq 0$
6. $a^{0}= 1 ; a \neq 0$

$a^{n-n}= \frac {a^{n}}{a^{n}}= 1$

7. $a^{-n}= \frac {1}{a^{n}}; a \neq 0$

$a^{0-n}=\frac {a^{0}}{a^{n}}= a^{-n}$

8. $a^{\frac {m}{n}}= \sqrt[n]{a^{m}}$

Persamaan Pangkat:

1. Jika $a^{f(x)} = a^{g(x)} \Leftrightarrow$ f(x) = g(x)
2. Jika $a^{f(x)} = a^{p} \Leftrightarrow$ f(x) = p

berlaku untuk a > 0 dan $a \neq 1$

Pertidaksamaan Pangkat:

Untuk a > 1

1. Jika $a^{f(x)} > a^{g(x)} \Leftrightarrow$ f(x) > g(x)
2. Jika $a^{f(x)} < a^{g(x)} \Leftrightarrow$ f(x) < g(x)

Untuk 0 < a < 1

1. Jika $a^{f(x)} > a^{g(x)} \Leftrightarrow$ f(x) < g(x)
2. Jika $a^{f(x)} < a^{g(x)} \Leftrightarrow$ f(x) > g(x)

This entry was posted on Wednesday, August 29th, 2012 at 3:43 am and is filed under Matematika SMA. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

What is 6 + 13 ?
IMPORTANT! To be able to proceed, you need to solve the following simple math (so we know that you are a human) :-)