Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{2}}\right)^{\frac{5}{2}}\\= y^{ \frac{1}{2} . \frac{5}{2} }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
2. \(\left(q^{\frac{1}{2}}\right)^{1}\\= q^{ \frac{1}{2} . 1 }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
3. \(\left(a^{\frac{4}{5}}\right)^{\frac{-3}{5}}\\= a^{ \frac{4}{5} . (\frac{-3}{5}) }= a^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ a^{12} }}=\frac{1}{\sqrt[25]{ a^{12} }}. \color{purple}{\frac{\sqrt[25]{ a^{13} }}{\sqrt[25]{ a^{13} }}} \\=\frac{\sqrt[25]{ a^{13} }}{a}\\---------------\)
4. \(\left(q^{-2}\right)^{\frac{-1}{2}}\\= q^{ -2 . (\frac{-1}{2}) }= q^{1}\\\\---------------\)
5. \(\left(y^{\frac{4}{3}}\right)^{\frac{4}{3}}\\= y^{ \frac{4}{3} . \frac{4}{3} }= y^{\frac{16}{9}}\\=\sqrt[9]{ y^{16} }=y.\sqrt[9]{ y^{7} }\\---------------\)
6. \(\left(y^{\frac{-1}{6}}\right)^{\frac{2}{3}}\\= y^{ \frac{-1}{6} . \frac{2}{3} }= y^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ y }}=\frac{1}{\sqrt[9]{ y }}. \color{purple}{\frac{\sqrt[9]{ y^{8} }}{\sqrt[9]{ y^{8} }}} \\=\frac{\sqrt[9]{ y^{8} }}{y}\\---------------\)
7. \(\left(a^{\frac{4}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{4}{3} . (\frac{-2}{3}) }= a^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ a^{8} }}=\frac{1}{\sqrt[9]{ a^{8} }}. \color{purple}{\frac{\sqrt[9]{ a }}{\sqrt[9]{ a }}} \\=\frac{\sqrt[9]{ a }}{a}\\---------------\)
8. \(\left(q^{\frac{5}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{5}{2} . \frac{1}{2} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
9. \(\left(y^{\frac{1}{3}}\right)^{\frac{-5}{6}}\\= y^{ \frac{1}{3} . (\frac{-5}{6}) }= y^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ y^{5} }}=\frac{1}{\sqrt[18]{ y^{5} }}. \color{purple}{\frac{\sqrt[18]{ y^{13} }}{\sqrt[18]{ y^{13} }}} \\=\frac{\sqrt[18]{ y^{13} }}{|y|}\\---------------\)
10. \(\left(y^{\frac{-3}{4}}\right)^{\frac{-4}{5}}\\= y^{ \frac{-3}{4} . (\frac{-4}{5}) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
11. \(\left(y^{\frac{-1}{5}}\right)^{\frac{3}{5}}\\= y^{ \frac{-1}{5} . \frac{3}{5} }= y^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ y^{3} }}=\frac{1}{\sqrt[25]{ y^{3} }}. \color{purple}{\frac{\sqrt[25]{ y^{22} }}{\sqrt[25]{ y^{22} }}} \\=\frac{\sqrt[25]{ y^{22} }}{y}\\---------------\)
12. \(\left(q^{\frac{2}{5}}\right)^{\frac{-1}{6}}\\= q^{ \frac{2}{5} . (\frac{-1}{6}) }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)