Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{4}{3}}\right)^{\frac{-1}{4}}\\= a^{ \frac{4}{3} . (\frac{-1}{4}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
2. \(\left(x^{-1}\right)^{\frac{2}{3}}\\= x^{ -1 . \frac{2}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
3. \(\left(y^{1}\right)^{\frac{-1}{2}}\\= y^{ 1 . (\frac{-1}{2}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
4. \(\left(q^{\frac{2}{5}}\right)^{\frac{-3}{5}}\\= q^{ \frac{2}{5} . (\frac{-3}{5}) }= q^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ q^{6} }}=\frac{1}{\sqrt[25]{ q^{6} }}. \color{purple}{\frac{\sqrt[25]{ q^{19} }}{\sqrt[25]{ q^{19} }}} \\=\frac{\sqrt[25]{ q^{19} }}{q}\\---------------\)
5. \(\left(a^{-1}\right)^{\frac{3}{5}}\\= a^{ -1 . \frac{3}{5} }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
6. \(\left(q^{\frac{2}{5}}\right)^{\frac{-5}{6}}\\= q^{ \frac{2}{5} . (\frac{-5}{6}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
7. \(\left(y^{\frac{-1}{5}}\right)^{\frac{3}{5}}\\= y^{ \frac{-1}{5} . \frac{3}{5} }= y^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ y^{3} }}=\frac{1}{\sqrt[25]{ y^{3} }}. \color{purple}{\frac{\sqrt[25]{ y^{22} }}{\sqrt[25]{ y^{22} }}} \\=\frac{\sqrt[25]{ y^{22} }}{y}\\---------------\)
8. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-4}{3}}\\= x^{ \frac{-2}{3} . (\frac{-4}{3}) }= x^{\frac{8}{9}}\\=\sqrt[9]{ x^{8} }\\---------------\)
9. \(\left(y^{\frac{2}{3}}\right)^{\frac{-3}{4}}\\= y^{ \frac{2}{3} . (\frac{-3}{4}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
10. \(\left(a^{\frac{1}{3}}\right)^{1}\\= a^{ \frac{1}{3} . 1 }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
11. \(\left(q^{1}\right)^{\frac{-1}{3}}\\= q^{ 1 . (\frac{-1}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
12. \(\left(q^{\frac{3}{2}}\right)^{\frac{-1}{6}}\\= q^{ \frac{3}{2} . (\frac{-1}{6}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)