Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{3}}\right)^{-1}\\= y^{ \frac{1}{3} . (-1) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
2. \(\left(q^{\frac{1}{3}}\right)^{\frac{3}{4}}\\= q^{ \frac{1}{3} . \frac{3}{4} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
3. \(\left(y^{\frac{1}{2}}\right)^{\frac{3}{4}}\\= y^{ \frac{1}{2} . \frac{3}{4} }= y^{\frac{3}{8}}\\=\sqrt[8]{ y^{3} }\\---------------\)
4. \(\left(y^{\frac{5}{6}}\right)^{\frac{4}{5}}\\= y^{ \frac{5}{6} . \frac{4}{5} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
5. \(\left(q^{\frac{1}{2}}\right)^{\frac{-3}{4}}\\= q^{ \frac{1}{2} . (\frac{-3}{4}) }= q^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ q^{3} }}=\frac{1}{\sqrt[8]{ q^{3} }}. \color{purple}{\frac{\sqrt[8]{ q^{5} }}{\sqrt[8]{ q^{5} }}} \\=\frac{\sqrt[8]{ q^{5} }}{|q|}\\---------------\)
6. \(\left(x^{\frac{1}{3}}\right)^{\frac{-5}{4}}\\= x^{ \frac{1}{3} . (\frac{-5}{4}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
7. \(\left(y^{\frac{-1}{4}}\right)^{-1}\\= y^{ \frac{-1}{4} . (-1) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
8. \(\left(a^{\frac{2}{5}}\right)^{\frac{-3}{5}}\\= a^{ \frac{2}{5} . (\frac{-3}{5}) }= a^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ a^{6} }}=\frac{1}{\sqrt[25]{ a^{6} }}. \color{purple}{\frac{\sqrt[25]{ a^{19} }}{\sqrt[25]{ a^{19} }}} \\=\frac{\sqrt[25]{ a^{19} }}{a}\\---------------\)
9. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-1}{2} . (\frac{-2}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
10. \(\left(q^{\frac{5}{3}}\right)^{\frac{5}{2}}\\= q^{ \frac{5}{3} . \frac{5}{2} }= q^{\frac{25}{6}}\\=\sqrt[6]{ q^{25} }=|q^{4}|.\sqrt[6]{ q }\\---------------\)
11. \(\left(y^{\frac{4}{3}}\right)^{1}\\= y^{ \frac{4}{3} . 1 }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
12. \(\left(x^{-2}\right)^{\frac{1}{6}}\\= x^{ -2 . \frac{1}{6} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)