Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{-2}\right)^{\frac{-1}{6}}\\= x^{ -2 . (\frac{-1}{6}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
2. \(\left(x^{\frac{-3}{2}}\right)^{\frac{-5}{4}}\\= x^{ \frac{-3}{2} . (\frac{-5}{4}) }= x^{\frac{15}{8}}\\=\sqrt[8]{ x^{15} }=|x|.\sqrt[8]{ x^{7} }\\---------------\)
3. \(\left(x^{\frac{5}{4}}\right)^{-2}\\= x^{ \frac{5}{4} . (-2) }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
4. \(\left(x^{\frac{2}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{2}{3} . \frac{1}{2} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
5. \(\left(a^{\frac{1}{4}}\right)^{\frac{3}{4}}\\= a^{ \frac{1}{4} . \frac{3}{4} }= a^{\frac{3}{16}}\\=\sqrt[16]{ a^{3} }\\---------------\)
6. \(\left(x^{\frac{-3}{4}}\right)^{\frac{-4}{5}}\\= x^{ \frac{-3}{4} . (\frac{-4}{5}) }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
7. \(\left(a^{\frac{-2}{5}}\right)^{1}\\= a^{ \frac{-2}{5} . 1 }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
8. \(\left(y^{\frac{5}{3}}\right)^{1}\\= y^{ \frac{5}{3} . 1 }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
9. \(\left(a^{\frac{5}{6}}\right)^{\frac{5}{3}}\\= a^{ \frac{5}{6} . \frac{5}{3} }= a^{\frac{25}{18}}\\=\sqrt[18]{ a^{25} }=|a|.\sqrt[18]{ a^{7} }\\---------------\)
10. \(\left(x^{\frac{1}{4}}\right)^{\frac{5}{3}}\\= x^{ \frac{1}{4} . \frac{5}{3} }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
11. \(\left(x^{\frac{1}{2}}\right)^{-1}\\= x^{ \frac{1}{2} . (-1) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
12. \(\left(a^{\frac{-1}{2}}\right)^{2}\\= a^{ \frac{-1}{2} . 2 }= a^{-1}\\=\frac{1}{a}\\---------------\)