Zadanie 1
7*\sqrt[5]7=7*7^{\frac{1}{5}}=7^{1+\frac{1}{5}}=7^{\frac{6}{5}}
Zadanie 2
Zapisz liczbę w postaci a^x, gdzie a ∈ N, x ∈ W.
a)
(\sqrt5)^3=(5^{\frac{1}{2}})^3=5^{\frac{3}{2}}
b)
\sqrt[3]3*\sqrt3=3^{\frac{1}{3}}*3^{\frac{1}{2}}=3^{\frac{2}{6}+\frac{3}{6}}=3^{\frac{5}{6}}
c)
2:8^{\frac{2}{3}}=2:(2^3)^{\frac{2}{3}}=2:2^2=2^{1-2}=2^{-1}
d)
3^{\frac{1}{8}}*12^{\frac{3}{4}}:\sqrt8=3^{\frac{1}{8}}*3^{\frac{3}{4}}*4^{\frac{3}{4}}:8^{\frac{1}{2}}=3^{\frac{1+6}{8}}*(2^2)^{\frac{3}{4}}:(2^3)^{\frac{1}{2}}=3^{\frac{7}{8}}*2^{\frac{3}{2}-\frac{3}{2}}=3^{\frac{7}{8}}*2^0=3^{\frac{7}{8}}*1=3^{\frac{7}{8}}
3^{\frac{1}{2}}*9^{\frac{1}{2}}*\sqrt3=3^{\frac{1}{2}}*(3^2)^{\frac{1}{2}}*3^{\frac{1}{2}}=3^{\frac{1}{2}+1+\frac{1}{2}}=3^2