Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{6}}\right)^{1}\\= q^{ \frac{1}{6} . 1 }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
2. \(\left(q^{\frac{4}{3}}\right)^{\frac{5}{3}}\\= q^{ \frac{4}{3} . \frac{5}{3} }= q^{\frac{20}{9}}\\=\sqrt[9]{ q^{20} }=q^{2}.\sqrt[9]{ q^{2} }\\---------------\)
3. \(\left(x^{\frac{3}{5}}\right)^{\frac{-3}{4}}\\= x^{ \frac{3}{5} . (\frac{-3}{4}) }= x^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ x^{9} }}=\frac{1}{\sqrt[20]{ x^{9} }}. \color{purple}{\frac{\sqrt[20]{ x^{11} }}{\sqrt[20]{ x^{11} }}} \\=\frac{\sqrt[20]{ x^{11} }}{|x|}\\---------------\)
4. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-2}{5} . (\frac{-1}{2}) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
5. \(\left(x^{\frac{5}{2}}\right)^{\frac{5}{3}}\\= x^{ \frac{5}{2} . \frac{5}{3} }= x^{\frac{25}{6}}\\=\sqrt[6]{ x^{25} }=|x^{4}|.\sqrt[6]{ x }\\---------------\)
6. \(\left(a^{-2}\right)^{\frac{4}{5}}\\= a^{ -2 . \frac{4}{5} }= a^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ a^{8} }}\\=\frac{1}{a.\sqrt[5]{ a^{3} }}=\frac{1}{a.\sqrt[5]{ a^{3} }} \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a^{2}}\\---------------\)
7. \(\left(a^{-1}\right)^{\frac{2}{3}}\\= a^{ -1 . \frac{2}{3} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
8. \(\left(q^{\frac{3}{2}}\right)^{\frac{-5}{6}}\\= q^{ \frac{3}{2} . (\frac{-5}{6}) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
9. \(\left(a^{-1}\right)^{\frac{3}{4}}\\= a^{ -1 . \frac{3}{4} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
10. \(\left(a^{\frac{-1}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{5} . (\frac{-1}{2}) }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
11. \(\left(q^{\frac{3}{4}}\right)^{\frac{1}{2}}\\= q^{ \frac{3}{4} . \frac{1}{2} }= q^{\frac{3}{8}}\\=\sqrt[8]{ q^{3} }\\---------------\)
12. \(\left(q^{-1}\right)^{\frac{1}{5}}\\= q^{ -1 . \frac{1}{5} }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)