Question

Scrieți ca o singura putere:
a) (1/3)^2 × (1/3)^3;
b) (7/5) × (7/5)^2;
c) (9/4)^3 × (9/4)^5;
d) (8/3)^5 : (8/3)^3;
e) (13/6)^12 : (13/6)^9;
f) (2/5)^5 : (2/5)^2;
g) (4/11)^10 : (4/11)^6 : (4/11).
​

Answer 1

Răspuns:

$a) \: (\frac{1}{3} ) {}^{2} \times (\frac{1}{3} ) {}^{3 } = ( \frac{1}{3} ) {}^{5}$

$b) \: \frac{7}{5} \times ( \frac{7}{5} ) {}^{2} = ( \frac{7}{5} ) {}^{3}$

$c) \: ( \frac{9}{4} ) {}^{3} \times ( \frac{9}{4} ) {}^{5} = (\frac{9}{4} ) {}^{8}$

$d) \: ( \frac{8}{3} ) {}^{5} \div ( \frac{8}{3} ) {}^{3} = ( \frac{8}{3} ) {}^{2}$

$e) \: ( \frac{13}{6} ) {}^{12} \div ( \frac{13}{6} ) {}^{9} = ( \frac{13}{6} ) {}^{3}$

$f) \: ( \frac{2}{5} ) {}^{5} \div (\frac{2}{5} ) {}^{2} = ( \frac{2}{5} ) {}^{3}$

$g) \: ( \frac{4}{11} ) {}^{10} \div (\frac{4}{11} ) {}^{6} \div \frac{4}{11} = ( \frac{4}{11} ) {}^{4} \div \frac{4}{11} = ( \frac{4}{11} ) {}^{3}$

Explicație pas cu pas:

$(\frac{x}{y} ) {}^{n} \times ( \frac{x}{y} ) {}^{m} = ( \frac{x}{y} ) {}^{n + m}$

$( \frac{x}{y} ) {}^{n} \div ( \frac{x}{y} ) {}^{m} = ( \frac{x}{y} ) {}^{n - m}$