Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{6}}\right)^{\frac{2}{3}}\\= y^{ \frac{-1}{6} . \frac{2}{3} }= y^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ y }}=\frac{1}{\sqrt[9]{ y }}. \color{purple}{\frac{\sqrt[9]{ y^{8} }}{\sqrt[9]{ y^{8} }}} \\=\frac{\sqrt[9]{ y^{8} }}{y}\\---------------\)
2. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-4}{3}}\\= y^{ \frac{-1}{2} . (\frac{-4}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
3. \(\left(q^{-1}\right)^{\frac{1}{3}}\\= q^{ -1 . \frac{1}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
4. \(\left(a^{\frac{-2}{3}}\right)^{\frac{4}{5}}\\= a^{ \frac{-2}{3} . \frac{4}{5} }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
5. \(\left(q^{1}\right)^{\frac{-1}{2}}\\= q^{ 1 . (\frac{-1}{2}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
6. \(\left(y^{\frac{1}{6}}\right)^{\frac{-1}{3}}\\= y^{ \frac{1}{6} . (\frac{-1}{3}) }= y^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ y }}=\frac{1}{\sqrt[18]{ y }}. \color{purple}{\frac{\sqrt[18]{ y^{17} }}{\sqrt[18]{ y^{17} }}} \\=\frac{\sqrt[18]{ y^{17} }}{|y|}\\---------------\)
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. \(\left(x^{\frac{-2}{3}}\right)^{2}\\= x^{ \frac{-2}{3} . 2 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
9. \(\left(a^{\frac{1}{6}}\right)^{1}\\= a^{ \frac{1}{6} . 1 }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
10. \(\left(a^{\frac{5}{2}}\right)^{\frac{-2}{3}}\\= a^{ \frac{5}{2} . (\frac{-2}{3}) }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
11. \(\left(q^{\frac{1}{3}}\right)^{\frac{3}{4}}\\= q^{ \frac{1}{3} . \frac{3}{4} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
12. \(\left(y^{\frac{-1}{5}}\right)^{1}\\= y^{ \frac{-1}{5} . 1 }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)