Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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