Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{3}}\right)^{\frac{4}{3}}\\= q^{ \frac{-1}{3} . \frac{4}{3} }= q^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ q^{4} }}=\frac{1}{\sqrt[9]{ q^{4} }}. \color{purple}{\frac{\sqrt[9]{ q^{5} }}{\sqrt[9]{ q^{5} }}} \\=\frac{\sqrt[9]{ q^{5} }}{q}\\---------------\)
2. \(\left(q^{\frac{1}{3}}\right)^{-1}\\= q^{ \frac{1}{3} . (-1) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
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. \(\left(a^{\frac{1}{6}}\right)^{\frac{-1}{5}}\\= a^{ \frac{1}{6} . (\frac{-1}{5}) }= a^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ a }}=\frac{1}{\sqrt[30]{ a }}. \color{purple}{\frac{\sqrt[30]{ a^{29} }}{\sqrt[30]{ a^{29} }}} \\=\frac{\sqrt[30]{ a^{29} }}{|a|}\\---------------\)
5. \(\left(y^{\frac{-4}{3}}\right)^{\frac{-1}{6}}\\= y^{ \frac{-4}{3} . (\frac{-1}{6}) }= y^{\frac{2}{9}}\\=\sqrt[9]{ y^{2} }\\---------------\)
6. \(\left(x^{\frac{-1}{4}}\right)^{\frac{-3}{2}}\\= x^{ \frac{-1}{4} . (\frac{-3}{2}) }= x^{\frac{3}{8}}\\=\sqrt[8]{ x^{3} }\\---------------\)
7. \(\left(a^{\frac{-5}{2}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-5}{2} . (\frac{-4}{3}) }= a^{\frac{10}{3}}\\=\sqrt[3]{ a^{10} }=a^{3}.\sqrt[3]{ a }\\---------------\)
8. \(\left(x^{\frac{-1}{2}}\right)^{\frac{2}{3}}\\= x^{ \frac{-1}{2} . \frac{2}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
9. \(\left(q^{\frac{-1}{5}}\right)^{\frac{1}{4}}\\= q^{ \frac{-1}{5} . \frac{1}{4} }= q^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ q }}=\frac{1}{\sqrt[20]{ q }}. \color{purple}{\frac{\sqrt[20]{ q^{19} }}{\sqrt[20]{ q^{19} }}} \\=\frac{\sqrt[20]{ q^{19} }}{|q|}\\---------------\)
10. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-1}{4}}\\= y^{ \frac{-2}{3} . (\frac{-1}{4}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
11. \(\left(a^{\frac{1}{4}}\right)^{\frac{2}{5}}\\= a^{ \frac{1}{4} . \frac{2}{5} }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
12. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-1}{4}}\\= a^{ \frac{-2}{5} . (\frac{-1}{4}) }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)