Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{2}{3}}\right)^{\frac{-1}{3}}\\= x^{ \frac{2}{3} . (\frac{-1}{3}) }= x^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ x^{2} }}=\frac{1}{\sqrt[9]{ x^{2} }}. \color{purple}{\frac{\sqrt[9]{ x^{7} }}{\sqrt[9]{ x^{7} }}} \\=\frac{\sqrt[9]{ x^{7} }}{x}\\---------------\)
2. \(\left(q^{1}\right)^{\frac{1}{2}}\\= q^{ 1 . \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
3. \(\left(y^{-1}\right)^{\frac{-1}{5}}\\= y^{ -1 . (\frac{-1}{5}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
4. \(\left(x^{\frac{-2}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{-2}{3} . \frac{1}{2} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
5. \(\left(x^{\frac{-3}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-3}{5} . (\frac{-1}{2}) }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
6. \(\left(q^{\frac{5}{4}}\right)^{\frac{2}{3}}\\= q^{ \frac{5}{4} . \frac{2}{3} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
7. \(\left(a^{-1}\right)^{\frac{3}{4}}\\= a^{ -1 . \frac{3}{4} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
8. \(\left(a^{\frac{-1}{3}}\right)^{\frac{3}{4}}\\= a^{ \frac{-1}{3} . \frac{3}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
9. \(\left(a^{\frac{3}{4}}\right)^{\frac{-5}{6}}\\= a^{ \frac{3}{4} . (\frac{-5}{6}) }= a^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ a^{5} }}=\frac{1}{\sqrt[8]{ a^{5} }}. \color{purple}{\frac{\sqrt[8]{ a^{3} }}{\sqrt[8]{ a^{3} }}} \\=\frac{\sqrt[8]{ a^{3} }}{|a|}\\---------------\)
10. \(\left(q^{\frac{3}{5}}\right)^{\frac{5}{4}}\\= q^{ \frac{3}{5} . \frac{5}{4} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
11. \(\left(a^{\frac{3}{5}}\right)^{\frac{3}{5}}\\= a^{ \frac{3}{5} . \frac{3}{5} }= a^{\frac{9}{25}}\\=\sqrt[25]{ a^{9} }\\---------------\)
12. \(\left(y^{\frac{-2}{5}}\right)^{\frac{4}{5}}\\= y^{ \frac{-2}{5} . \frac{4}{5} }= y^{\frac{-8}{25}}\\=\frac{1}{\sqrt[25]{ y^{8} }}=\frac{1}{\sqrt[25]{ y^{8} }}. \color{purple}{\frac{\sqrt[25]{ y^{17} }}{\sqrt[25]{ y^{17} }}} \\=\frac{\sqrt[25]{ y^{17} }}{y}\\---------------\)