Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{5}{2}}\right)^{-1}\\= x^{ \frac{5}{2} . (-1) }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
2. \(\left(q^{1}\right)^{-1}\\= q^{ 1 . (-1) }= q^{-1}\\=\frac{1}{q}\\---------------\)
3. \(\left(q^{\frac{-1}{2}}\right)^{\frac{1}{6}}\\= q^{ \frac{-1}{2} . \frac{1}{6} }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
4. \(\left(q^{-1}\right)^{\frac{1}{6}}\\= q^{ -1 . \frac{1}{6} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
5. \(\left(a^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= a^{ \frac{1}{2} . \frac{1}{2} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
6. \(\left(y^{\frac{-1}{5}}\right)^{\frac{-5}{4}}\\= y^{ \frac{-1}{5} . (\frac{-5}{4}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
7. \(\left(a^{\frac{2}{5}}\right)^{\frac{-5}{3}}\\= a^{ \frac{2}{5} . (\frac{-5}{3}) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
8. \(\left(q^{1}\right)^{\frac{5}{2}}\\= q^{ 1 . \frac{5}{2} }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
9. \(\left(x^{\frac{-5}{6}}\right)^{\frac{1}{3}}\\= x^{ \frac{-5}{6} . \frac{1}{3} }= x^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ x^{5} }}=\frac{1}{\sqrt[18]{ x^{5} }}. \color{purple}{\frac{\sqrt[18]{ x^{13} }}{\sqrt[18]{ x^{13} }}} \\=\frac{\sqrt[18]{ x^{13} }}{|x|}\\---------------\)
10. \(\left(x^{1}\right)^{\frac{4}{3}}\\= x^{ 1 . \frac{4}{3} }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
11. \(\left(q^{-1}\right)^{\frac{-5}{6}}\\= q^{ -1 . (\frac{-5}{6}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
12. \(\left(a^{\frac{-3}{5}}\right)^{\frac{2}{5}}\\= a^{ \frac{-3}{5} . \frac{2}{5} }= a^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ a^{6} }}=\frac{1}{\sqrt[25]{ a^{6} }}. \color{purple}{\frac{\sqrt[25]{ a^{19} }}{\sqrt[25]{ a^{19} }}} \\=\frac{\sqrt[25]{ a^{19} }}{a}\\---------------\)