Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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