Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{1}{3}}\right)^{\frac{-2}{5}}\\= a^{ \frac{1}{3} . (\frac{-2}{5}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
2. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-4}{3}}\\= y^{ \frac{-2}{5} . (\frac{-4}{3}) }= y^{\frac{8}{15}}\\=\sqrt[15]{ y^{8} }\\---------------\)
3. \(\left(y^{\frac{-4}{5}}\right)^{1}\\= y^{ \frac{-4}{5} . 1 }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
4. \(\left(a^{\frac{-3}{4}}\right)^{\frac{1}{2}}\\= a^{ \frac{-3}{4} . \frac{1}{2} }= a^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ a^{3} }}=\frac{1}{\sqrt[8]{ a^{3} }}. \color{purple}{\frac{\sqrt[8]{ a^{5} }}{\sqrt[8]{ a^{5} }}} \\=\frac{\sqrt[8]{ a^{5} }}{|a|}\\---------------\)
5. \(\left(q^{\frac{1}{3}}\right)^{\frac{2}{3}}\\= q^{ \frac{1}{3} . \frac{2}{3} }= q^{\frac{2}{9}}\\=\sqrt[9]{ q^{2} }\\---------------\)
6. \(\left(q^{\frac{-5}{6}}\right)^{\frac{1}{3}}\\= q^{ \frac{-5}{6} . \frac{1}{3} }= q^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ q^{5} }}=\frac{1}{\sqrt[18]{ q^{5} }}. \color{purple}{\frac{\sqrt[18]{ q^{13} }}{\sqrt[18]{ q^{13} }}} \\=\frac{\sqrt[18]{ q^{13} }}{|q|}\\---------------\)
7. \(\left(y^{\frac{1}{2}}\right)^{\frac{-4}{3}}\\= y^{ \frac{1}{2} . (\frac{-4}{3}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
8. \(\left(a^{\frac{5}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{5}{3} . (\frac{-1}{2}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
9. \(\left(a^{\frac{-3}{2}}\right)^{\frac{5}{6}}\\= a^{ \frac{-3}{2} . \frac{5}{6} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
10. \(\left(a^{\frac{5}{6}}\right)^{\frac{1}{4}}\\= a^{ \frac{5}{6} . \frac{1}{4} }= a^{\frac{5}{24}}\\=\sqrt[24]{ a^{5} }\\---------------\)
11. \(\left(q^{\frac{-1}{5}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-1}{5} . (\frac{-1}{3}) }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
12. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-1}{2} . (\frac{-1}{3}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)