Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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