Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

1. \(\left(y^{\frac{1}{2}}\right)^{\frac{5}{6}}\)
2. \(\left(a^{\frac{4}{3}}\right)^{\frac{1}{6}}\)
3. \(\left(a^{\frac{2}{3}}\right)^{\frac{4}{3}}\)
4. \(\left(y^{\frac{1}{4}}\right)^{\frac{-5}{4}}\)
5. \(\left(x^{1}\right)^{\frac{-1}{3}}\)
6. \(\left(y^{1}\right)^{\frac{1}{2}}\)
7. \(\left(x^{\frac{1}{5}}\right)^{\frac{-1}{3}}\)
8. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\)
9. \(\left(y^{\frac{-5}{2}}\right)^{\frac{-4}{3}}\)
10. \(\left(y^{\frac{-1}{2}}\right)^{\frac{3}{5}}\)
11. \(\left(a^{\frac{3}{5}}\right)^{\frac{4}{5}}\)
12. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{2}}\)

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{2}}\right)^{\frac{5}{6}}\\= y^{ \frac{1}{2} . \frac{5}{6} }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
2. \(\left(a^{\frac{4}{3}}\right)^{\frac{1}{6}}\\= a^{ \frac{4}{3} . \frac{1}{6} }= a^{\frac{2}{9}}\\=\sqrt[9]{ a^{2} }\\---------------\)
3. \(\left(a^{\frac{2}{3}}\right)^{\frac{4}{3}}\\= a^{ \frac{2}{3} . \frac{4}{3} }= a^{\frac{8}{9}}\\=\sqrt[9]{ a^{8} }\\---------------\)
4. \(\left(y^{\frac{1}{4}}\right)^{\frac{-5}{4}}\\= y^{ \frac{1}{4} . (\frac{-5}{4}) }= y^{\frac{-5}{16}}\\=\frac{1}{\sqrt[16]{ y^{5} }}=\frac{1}{\sqrt[16]{ y^{5} }}. \color{purple}{\frac{\sqrt[16]{ y^{11} }}{\sqrt[16]{ y^{11} }}} \\=\frac{\sqrt[16]{ y^{11} }}{|y|}\\---------------\)
5. \(\left(x^{1}\right)^{\frac{-1}{3}}\\= x^{ 1 . (\frac{-1}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
6. \(\left(y^{1}\right)^{\frac{1}{2}}\\= y^{ 1 . \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
7. \(\left(x^{\frac{1}{5}}\right)^{\frac{-1}{3}}\\= x^{ \frac{1}{5} . (\frac{-1}{3}) }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
8. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-2}{3} . (\frac{-1}{2}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
9. \(\left(y^{\frac{-5}{2}}\right)^{\frac{-4}{3}}\\= y^{ \frac{-5}{2} . (\frac{-4}{3}) }= y^{\frac{10}{3}}\\=\sqrt[3]{ y^{10} }=y^{3}.\sqrt[3]{ y }\\---------------\)
10. \(\left(y^{\frac{-1}{2}}\right)^{\frac{3}{5}}\\= y^{ \frac{-1}{2} . \frac{3}{5} }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
11. \(\left(a^{\frac{3}{5}}\right)^{\frac{4}{5}}\\= a^{ \frac{3}{5} . \frac{4}{5} }= a^{\frac{12}{25}}\\=\sqrt[25]{ a^{12} }\\---------------\)
12. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{-1}{2} . \frac{1}{2} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)