Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-1}{3}}\\= x^{ \frac{-1}{2} . (\frac{-1}{3}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
2. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-1}{3} . (\frac{-1}{6}) }= a^{\frac{1}{18}}\\=\sqrt[18]{ a }\\---------------\)
3. \(\left(y^{2}\right)^{\frac{-3}{5}}\\= y^{ 2 . (\frac{-3}{5}) }= y^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ y^{6} }}\\=\frac{1}{y.\sqrt[5]{ y }}=\frac{1}{y.\sqrt[5]{ y }} \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y^{2}}\\---------------\)
4. \(\left(a^{\frac{3}{5}}\right)^{\frac{-1}{3}}\\= a^{ \frac{3}{5} . (\frac{-1}{3}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
5. \(\left(y^{\frac{-1}{4}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{4} . (\frac{-1}{2}) }= y^{\frac{1}{8}}\\=\sqrt[8]{ y }\\---------------\)
6. \(\left(x^{\frac{5}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{5}{3} . \frac{1}{2} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
7. \(\left(q^{\frac{1}{3}}\right)^{\frac{-3}{4}}\\= q^{ \frac{1}{3} . (\frac{-3}{4}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
8. \(\left(q^{\frac{-1}{3}}\right)^{-1}\\= q^{ \frac{-1}{3} . (-1) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
9. \(\left(q^{\frac{1}{3}}\right)^{\frac{-5}{4}}\\= q^{ \frac{1}{3} . (\frac{-5}{4}) }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
10. \(\left(x^{\frac{-1}{2}}\right)^{\frac{5}{2}}\\= x^{ \frac{-1}{2} . \frac{5}{2} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
11. \(\left(x^{\frac{-1}{5}}\right)^{\frac{2}{3}}\\= x^{ \frac{-1}{5} . \frac{2}{3} }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
12. \(\left(q^{\frac{3}{2}}\right)^{\frac{-3}{2}}\\= q^{ \frac{3}{2} . (\frac{-3}{2}) }= q^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ q^{9} }}\\=\frac{1}{|q^{2}|.\sqrt[4]{ q }}=\frac{1}{|q^{2}|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{3}|}\\---------------\)