Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{6}}\right)^{\frac{3}{4}}\\= x^{ \frac{-1}{6} . \frac{3}{4} }= x^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ x }}=\frac{1}{\sqrt[8]{ x }}. \color{purple}{\frac{\sqrt[8]{ x^{7} }}{\sqrt[8]{ x^{7} }}} \\=\frac{\sqrt[8]{ x^{7} }}{|x|}\\---------------\)
2. \(\left(q^{\frac{-2}{5}}\right)^{\frac{-5}{4}}\\= q^{ \frac{-2}{5} . (\frac{-5}{4}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
3. \(\left(q^{\frac{-5}{2}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-5}{2} . (\frac{-1}{3}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
4. \(\left(y^{\frac{1}{2}}\right)^{\frac{-1}{6}}\\= y^{ \frac{1}{2} . (\frac{-1}{6}) }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
5. \(\left(q^{\frac{5}{2}}\right)^{\frac{-2}{5}}\\= q^{ \frac{5}{2} . (\frac{-2}{5}) }= q^{-1}\\=\frac{1}{q}\\---------------\)
6. \(\left(q^{\frac{2}{5}}\right)^{\frac{5}{3}}\\= q^{ \frac{2}{5} . \frac{5}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
7. \(\left(a^{\frac{5}{3}}\right)^{\frac{3}{4}}\\= a^{ \frac{5}{3} . \frac{3}{4} }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
8. \(\left(y^{\frac{-5}{2}}\right)^{\frac{-5}{4}}\\= y^{ \frac{-5}{2} . (\frac{-5}{4}) }= y^{\frac{25}{8}}\\=\sqrt[8]{ y^{25} }=|y^{3}|.\sqrt[8]{ y }\\---------------\)
9. \(\left(y^{\frac{-2}{3}}\right)^{-1}\\= y^{ \frac{-2}{3} . (-1) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
10. \(\left(q^{\frac{1}{2}}\right)^{\frac{-1}{5}}\\= q^{ \frac{1}{2} . (\frac{-1}{5}) }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
11. \(\left(y^{\frac{-1}{3}}\right)^{\frac{5}{6}}\\= y^{ \frac{-1}{3} . \frac{5}{6} }= y^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ y^{5} }}=\frac{1}{\sqrt[18]{ y^{5} }}. \color{purple}{\frac{\sqrt[18]{ y^{13} }}{\sqrt[18]{ y^{13} }}} \\=\frac{\sqrt[18]{ y^{13} }}{|y|}\\---------------\)
12. \(\left(y^{1}\right)^{1}\\= y^{ 1 . 1 }= y^{1}\\\\---------------\)