Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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