Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-5}{2}}\right)^{\frac{4}{5}}\\= x^{ \frac{-5}{2} . \frac{4}{5} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
2. \(\left(q^{\frac{1}{4}}\right)^{\frac{1}{2}}\\= q^{ \frac{1}{4} . \frac{1}{2} }= q^{\frac{1}{8}}\\=\sqrt[8]{ q }\\---------------\)
3. \(\left(x^{-1}\right)^{-1}\\= x^{ -1 . (-1) }= x^{1}\\\\---------------\)
4. \(\left(y^{\frac{-3}{5}}\right)^{\frac{1}{5}}\\= y^{ \frac{-3}{5} . \frac{1}{5} }= y^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ y^{3} }}=\frac{1}{\sqrt[25]{ y^{3} }}. \color{purple}{\frac{\sqrt[25]{ y^{22} }}{\sqrt[25]{ y^{22} }}} \\=\frac{\sqrt[25]{ y^{22} }}{y}\\---------------\)
5. \(\left(x^{\frac{-2}{5}}\right)^{\frac{3}{2}}\\= x^{ \frac{-2}{5} . \frac{3}{2} }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
6. \(\left(y^{1}\right)^{\frac{4}{5}}\\= y^{ 1 . \frac{4}{5} }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
7. \(\left(y^{1}\right)^{\frac{5}{4}}\\= y^{ 1 . \frac{5}{4} }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
8. \(\left(x^{\frac{2}{3}}\right)^{\frac{5}{6}}\\= x^{ \frac{2}{3} . \frac{5}{6} }= x^{\frac{5}{9}}\\=\sqrt[9]{ x^{5} }\\---------------\)
9. \(\left(y^{\frac{-1}{5}}\right)^{\frac{1}{3}}\\= y^{ \frac{-1}{5} . \frac{1}{3} }= y^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ y }}=\frac{1}{\sqrt[15]{ y }}. \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y}\\---------------\)
10. \(\left(x^{\frac{-2}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{-2}{3} . \frac{1}{2} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
11. \(\left(x^{\frac{-1}{5}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-1}{5} . (\frac{-5}{6}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
12. \(\left(a^{\frac{1}{4}}\right)^{\frac{-4}{5}}\\= a^{ \frac{1}{4} . (\frac{-4}{5}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)