Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-5}{3}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-5}{3} . (\frac{-1}{3}) }= a^{\frac{5}{9}}\\=\sqrt[9]{ a^{5} }\\---------------\)
2. \(\left(x^{\frac{5}{6}}\right)^{-1}\\= x^{ \frac{5}{6} . (-1) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
3. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{5}}\\= y^{ \frac{1}{2} . \frac{1}{5} }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
4. \(\left(y^{\frac{-1}{6}}\right)^{\frac{2}{5}}\\= y^{ \frac{-1}{6} . \frac{2}{5} }= y^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ y }}=\frac{1}{\sqrt[15]{ y }}. \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y}\\---------------\)
5. \(\left(x^{\frac{1}{4}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{4} . \frac{1}{2} }= x^{\frac{1}{8}}\\=\sqrt[8]{ x }\\---------------\)
6. \(\left(q^{\frac{-5}{2}}\right)^{1}\\= q^{ \frac{-5}{2} . 1 }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
7. \(\left(q^{-1}\right)^{\frac{1}{3}}\\= q^{ -1 . \frac{1}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
8. \(\left(x^{\frac{3}{2}}\right)^{\frac{1}{6}}\\= x^{ \frac{3}{2} . \frac{1}{6} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
9. \(\left(y^{\frac{-1}{4}}\right)^{\frac{-3}{5}}\\= y^{ \frac{-1}{4} . (\frac{-3}{5}) }= y^{\frac{3}{20}}\\=\sqrt[20]{ y^{3} }\\---------------\)
10. \(\left(q^{\frac{1}{4}}\right)^{-1}\\= q^{ \frac{1}{4} . (-1) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
11. \(\left(a^{\frac{-5}{2}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-5}{2} . (\frac{-1}{3}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
12. \(\left(x^{1}\right)^{\frac{-1}{5}}\\= x^{ 1 . (\frac{-1}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)