Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{5}}\right)^{\frac{-5}{2}}\\= y^{ \frac{1}{5} . (\frac{-5}{2}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
2. \(\left(x^{\frac{3}{4}}\right)^{\frac{2}{3}}\\= x^{ \frac{3}{4} . \frac{2}{3} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
3. \(\left(x^{\frac{-2}{3}}\right)^{1}\\= x^{ \frac{-2}{3} . 1 }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
4. \(\left(q^{\frac{-3}{4}}\right)^{\frac{-4}{5}}\\= q^{ \frac{-3}{4} . (\frac{-4}{5}) }= q^{\frac{3}{5}}\\=\sqrt[5]{ q^{3} }\\---------------\)
5. \(\left(y^{\frac{-3}{4}}\right)^{\frac{-3}{4}}\\= y^{ \frac{-3}{4} . (\frac{-3}{4}) }= y^{\frac{9}{16}}\\=\sqrt[16]{ y^{9} }\\---------------\)
6. \(\left(x^{\frac{-3}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-3}{5} . (\frac{-1}{2}) }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
7. \(\left(y^{\frac{-4}{5}}\right)^{\frac{1}{6}}\\= y^{ \frac{-4}{5} . \frac{1}{6} }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
8. \(\left(q^{\frac{-5}{6}}\right)^{\frac{1}{2}}\\= q^{ \frac{-5}{6} . \frac{1}{2} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
9. \(\left(y^{1}\right)^{\frac{-1}{3}}\\= y^{ 1 . (\frac{-1}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
10. \(\left(y^{\frac{2}{3}}\right)^{\frac{-1}{5}}\\= y^{ \frac{2}{3} . (\frac{-1}{5}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
11. \(\left(y^{\frac{-3}{4}}\right)^{\frac{4}{5}}\\= y^{ \frac{-3}{4} . \frac{4}{5} }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
12. \(\left(y^{\frac{5}{3}}\right)^{\frac{5}{6}}\\= y^{ \frac{5}{3} . \frac{5}{6} }= y^{\frac{25}{18}}\\=\sqrt[18]{ y^{25} }=|y|.\sqrt[18]{ y^{7} }\\---------------\)