Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-1}{2} . (\frac{-5}{6}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
2. \(\left(q^{\frac{-5}{2}}\right)^{\frac{-5}{2}}\\= q^{ \frac{-5}{2} . (\frac{-5}{2}) }= q^{\frac{25}{4}}\\=\sqrt[4]{ q^{25} }=|q^{6}|.\sqrt[4]{ q }\\---------------\)
3. \(\left(y^{\frac{4}{3}}\right)^{\frac{3}{2}}\\= y^{ \frac{4}{3} . \frac{3}{2} }= y^{2}\\\\---------------\)
4. \(\left(x^{\frac{-1}{2}}\right)^{\frac{3}{2}}\\= x^{ \frac{-1}{2} . \frac{3}{2} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
5. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-5}{3}}\\= a^{ \frac{-2}{5} . (\frac{-5}{3}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
6. \(\left(q^{\frac{1}{5}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{5} . (\frac{-1}{3}) }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
7. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-4}{5} . (\frac{-5}{6}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
8. \(\left(x^{-1}\right)^{\frac{-1}{5}}\\= x^{ -1 . (\frac{-1}{5}) }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
9. \(\left(q^{\frac{-5}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-5}{3} . (\frac{-1}{2}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
10. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-2}{3} . (\frac{-2}{3}) }= a^{\frac{4}{9}}\\=\sqrt[9]{ a^{4} }\\---------------\)
11. \(\left(q^{\frac{2}{5}}\right)^{\frac{1}{4}}\\= q^{ \frac{2}{5} . \frac{1}{4} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
12. \(\left(x^{\frac{1}{5}}\right)^{\frac{1}{6}}\\= x^{ \frac{1}{5} . \frac{1}{6} }= x^{\frac{1}{30}}\\=\sqrt[30]{ x }\\---------------\)