Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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