Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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