Proszę o formę rozpisaną w załączniku.... Question from @Bartusiowy

Zadanie 1

a. $(\frac{7}{4})^{\frac{2}{5}}*(\frac{7}{4})^{\frac{3}{5}}=(\frac{7}{4})^{\frac{5}{5}}=\frac{7}{4}$

b. $3^{\frac{1}{3}}*3^{\frac{5}{3}}=3^{\frac{6}{3}}=3^{2}=9$

c. $2^{\frac{1}{2}}*8^{\frac{1}{2}}=2^{\frac{1}{2}}*(2^{3})^{\frac{1}{2}}=2^{\frac{1}{2}}*2^{\frac{3}{2}}=2^{2}=4$

d. $5^{\frac{1}{3}}*25^{\frac{1}{3}}=5^{\frac{1}{3}}*(5^{2})^{\frac{1}{3}}=5^{\frac{1}{3}}*5^{\frac{2}{3}}=5$

e. $108^{\frac{1}{3}}*2^{\frac{1}{3}}+7^{\frac{1}{3}}*49^{\frac{1}{3}}=(108*2)^{\frac{1}{3}}+7^{\frac{1}{3}}*7^{\frac{2}{3}}=216^{\frac{1}{3}}+7=$

$=(6^{3}})^{\frac{1}{3}}+7=6+7=13$

Zadanie 2

a. $64=8^{2}$

b. $1=8^{0}$

c. $2=8^{\frac{1}{3}}$

d. $4=8^{\frac{3}{2}}$

e. $\frac{1}{32}=8^{-\frac{5}{3}}$

f. $32=8^{\frac{5}{3}}$

g. $\frac{1}{2}=8^{-\frac{1}{3}}$

h. $\frac{1}{256}=8^{-\frac{8}{3}$

Zadanie 3

a. $x=(-3)^{3} \\ x=-27$

b. $x=(\frac{1}{4})^{4} \\ x=\frax{1}{16}$

c. $x=(\frac{3}{5})^{2} \\ x=\frac{9}{25}$

d. $x=(0,4)^{4} \\ x=0,0256$

e. $x^{2}=4 \\ x=2$

f. $x^{3}=125 \\ x=5$

g. $x^{-2}=\frac{1}{36} \\ x=6$

h. $2^{x}=4 \\ x=2$

i. $x^{x}=81 \\ x=4$

j. $(\frac{1}{4})^{x}=\frac{1}{64} \\ x=3$

Zadanie 4

a. $3^{3}*3^{\frac{1}{2}}*3^{-2}=3^{1\frac{1}{2}}$

b. $\sqrt[3]{9}*3^{2}*3^{0}*3^{\frac{1}{3}}=3^{\frac{2}{3}}*3^{2}*3^{\frac{1}{3}}=3^{3}$

c. $\sqrt{3^{3}}=3^{\frac{3}{2}}=3^{1\frac{1}{2}}$

d. $\sqrt{\sqrt[4]{3^{-5}}*\sqrt[5]{9}}}=(3^{-\frac{5}{4}}*3^{\frac{2}{5}})^{\frac{1}{2}}=3^{-\frac{5}{8}}*3^{\frac{1}{5}}=3^{-\frac{25}{40}+\frac{8}{40}}=3^{\frac{17}{40}}$

e. $125^{0,3}*25^{-\frac{1}{5}}*5^{\frac{1}{2}}=(5^{3})^{\frac{3}{10}}*(5^{2})^{-\frc{1}{5}}*5^{\frac{1}{2}}=5^{\frac{9}{10}}*5^{-\frac{2}{5}}*5^{\frac{1}{2}}=5$

f. $49^{\frac{1}{6}}*7^{-\frac{1}{4}}*7^{2}=(7^{2})^{\frac{1}{6}}*7^{-\frac{1}{4}}*7^{2}=7^{\frac{1}{3}-\frac{1}{4}+2}=7^{\frac{4}{12}-\frac{3}{12+2}=7^{2\frac{1}{12}}$