Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{4}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{4} . (\frac{-1}{3}) }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
2. \(\left(y^{1}\right)^{-1}\\= y^{ 1 . (-1) }= y^{-1}\\=\frac{1}{y}\\---------------\)
3. \(\left(q^{1}\right)^{\frac{2}{3}}\\= q^{ 1 . \frac{2}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
4. \(\left(y^{\frac{-1}{6}}\right)^{\frac{-4}{5}}\\= y^{ \frac{-1}{6} . (\frac{-4}{5}) }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
5. \(\left(x^{\frac{5}{3}}\right)^{\frac{1}{6}}\\= x^{ \frac{5}{3} . \frac{1}{6} }= x^{\frac{5}{18}}\\=\sqrt[18]{ x^{5} }\\---------------\)
6. \(\left(x^{\frac{-1}{4}}\right)^{\frac{5}{3}}\\= x^{ \frac{-1}{4} . \frac{5}{3} }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
7. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{3}}\\= q^{ \frac{1}{2} . \frac{1}{3} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
8. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{2} . \frac{1}{2} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
9. \(\left(y^{\frac{-1}{5}}\right)^{\frac{5}{3}}\\= y^{ \frac{-1}{5} . \frac{5}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
10. \(\left(x^{\frac{4}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{4}{5} . (\frac{-1}{2}) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
11. \(\left(x^{\frac{4}{5}}\right)^{\frac{2}{3}}\\= x^{ \frac{4}{5} . \frac{2}{3} }= x^{\frac{8}{15}}\\=\sqrt[15]{ x^{8} }\\---------------\)
12. \(\left(q^{\frac{1}{5}}\right)^{\frac{1}{4}}\\= q^{ \frac{1}{5} . \frac{1}{4} }= q^{\frac{1}{20}}\\=\sqrt[20]{ q }\\---------------\)