Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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