Rumus Pangkat Rasional

RUMUS PANGKAT RASIONAL

1. a^m . aⁿ = a^{m + n}
   
2. $\frac{a^m}{a^n}=a^{m\; -\; n}$
   
3. (a^m . b^m) = (a . b)^m
   
4. $\frac{a^m}{b^m}={\left(\frac{a}{b}\right)}^m$
   
5. (a^m)ⁿ = a^mn
   
6. a⁰ = 1   , a ≠ 0
7. $a^{-m}=\frac{1}{a^m}$
   
8. $a^{\frac{m}{n}}=\sqrt[n]{a^m}$
   
9. $a^{-\frac{m}{n}}=\frac{1}{\sqrt[n]{a^m}}$
   
10. $\sqrt[m]{a}.\sqrt[m]{b}=\sqrt[m]{ab}={ab}^{\frac{1}{m}}$
11. $\frac{\sqrt[m]{a}}{\sqrt[m]{b}}=\sqrt[m]{\frac{a}{b}}={\left(\frac{a}{b}\right)}^{\frac{1}{m}}$

Contoh Soal :
Sederhanakan bentuk bilangan berpangkat berikut :

1. 2⁵ x 2²
   
2. $\frac{2^3}{2^2}$
   
3. (3²)³
   

Jawab :

1. 2⁵ x 2² = 2^{5 + 2} = 2⁷
   
2. $\frac{2^3}{2^2}=2^{3\; -\; 2}=2^1=2$
   
3. (3²)³ = 3⁶