Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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