Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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