Odpowiedź :
Odpowiedź:
a)
[9⁻¹⁾³ * ⁶√3]/[√3⁻⁹ * 9²⁾³ * ∛27²] = [(3²)⁻¹⁾³ * 3¹⁾⁶]/[(3⁻⁹)¹⁾²*(3²)²⁾³ * 3 * 3] =
= (3⁻²⁾³ * 3¹⁾⁶)/(3⁻⁹⁾² * 3⁴⁾³ * 3²) = (3⁻⁴⁾⁶⁺¹⁾⁶)/(3⁻⁹⁾²⁺⁴⁾³⁺²) = 3⁻³⁾⁶/3⁻²⁷⁾⁶⁺⁸⁾⁶⁺² =
= 3⁻¹⁾²/3⁻¹⁹⁾⁶⁺² = 3⁻¹⁾²/3⁻¹⁹⁾⁶⁺¹²⁾⁶ = 3⁻¹⁾²/3⁻⁷⁾⁶ = 3⁻³⁾⁶/3⁻⁷⁾⁶ = 3⁻³⁾⁶⁺⁷⁾⁶ = 3⁴⁾⁶ = 3²⁾³
b)
3²⁾³ =∛3²= ∛9
c
Szczegółowe wyjaśnienie:
Odpowiedź:
[tex]\frac{9^{-\frac{1}{3}}*\sqrt[6]{3} }{\sqrt{3^{-9}}*9^{\frac{2}{3}}*\sqrt[3]{27^2} }=\frac{9^{(-\frac{1}{3}-\frac{2}{3})}*3^{\frac{1}{6}} }{3^{-\frac{9}{2} }*3^2}=\frac{9^{-1}*3^{\frac{1}{6}}}{3^{-\frac{5}{2}}} =\frac{3^{-2}*3^{\frac{1}{6}}}{3^{-\frac{5}{2}}}=3^{(-2+\frac{1}{6}+\frac{5}{2})}=3^{(-\frac{12}{6}+\frac{1}{6}+\frac{15}{6})}=3^{\frac{4}{6}}=3^{\frac{2}{3}} =\sqrt[3]{3^2}[/tex]
Szczegółowe wyjaśnienie: