Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{5}}\right)^{\frac{-3}{4}}\\= q^{ \frac{1}{5} . (\frac{-3}{4}) }= q^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ q^{3} }}=\frac{1}{\sqrt[20]{ q^{3} }}. \color{purple}{\frac{\sqrt[20]{ q^{17} }}{\sqrt[20]{ q^{17} }}} \\=\frac{\sqrt[20]{ q^{17} }}{|q|}\\---------------\)
2. \(\left(x^{\frac{-5}{3}}\right)^{\frac{3}{2}}\\= x^{ \frac{-5}{3} . \frac{3}{2} }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
3. \(\left(x^{\frac{5}{6}}\right)^{\frac{5}{3}}\\= x^{ \frac{5}{6} . \frac{5}{3} }= x^{\frac{25}{18}}\\=\sqrt[18]{ x^{25} }=|x|.\sqrt[18]{ x^{7} }\\---------------\)
4. \(\left(x^{-1}\right)^{1}\\= x^{ -1 . 1 }= x^{-1}\\=\frac{1}{x}\\---------------\)
5. \(\left(a^{\frac{5}{4}}\right)^{\frac{5}{6}}\\= a^{ \frac{5}{4} . \frac{5}{6} }= a^{\frac{25}{24}}\\=\sqrt[24]{ a^{25} }=|a|.\sqrt[24]{ a }\\---------------\)
6. \(\left(y^{\frac{-1}{3}}\right)^{1}\\= y^{ \frac{-1}{3} . 1 }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
7. \(\left(y^{\frac{-5}{2}}\right)^{\frac{-5}{4}}\\= y^{ \frac{-5}{2} . (\frac{-5}{4}) }= y^{\frac{25}{8}}\\=\sqrt[8]{ y^{25} }=|y^{3}|.\sqrt[8]{ y }\\---------------\)
8. \(\left(q^{\frac{-1}{2}}\right)^{1}\\= q^{ \frac{-1}{2} . 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
9. \(\left(y^{\frac{-5}{6}}\right)^{\frac{-5}{2}}\\= y^{ \frac{-5}{6} . (\frac{-5}{2}) }= y^{\frac{25}{12}}\\=\sqrt[12]{ y^{25} }=|y^{2}|.\sqrt[12]{ y }\\---------------\)
10. \(\left(a^{\frac{1}{5}}\right)^{\frac{-5}{4}}\\= a^{ \frac{1}{5} . (\frac{-5}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
11. \(\left(a^{\frac{-5}{6}}\right)^{\frac{-3}{5}}\\= a^{ \frac{-5}{6} . (\frac{-3}{5}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
12. \(\left(q^{\frac{-1}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{-1}{3} . \frac{1}{2} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)