Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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