Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-5}{4}}\right)^{\frac{-4}{5}}\\= x^{ \frac{-5}{4} . (\frac{-4}{5}) }= x^{1}\\\\---------------\)
2. \(\left(y^{\frac{5}{6}}\right)^{\frac{3}{2}}\\= y^{ \frac{5}{6} . \frac{3}{2} }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
3. \(\left(x^{\frac{-1}{6}}\right)^{\frac{3}{4}}\\= x^{ \frac{-1}{6} . \frac{3}{4} }= x^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ x }}=\frac{1}{\sqrt[8]{ x }}. \color{purple}{\frac{\sqrt[8]{ x^{7} }}{\sqrt[8]{ x^{7} }}} \\=\frac{\sqrt[8]{ x^{7} }}{|x|}\\---------------\)
4. \(\left(y^{1}\right)^{\frac{5}{3}}\\= y^{ 1 . \frac{5}{3} }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
5. \(\left(q^{\frac{5}{6}}\right)^{\frac{-4}{3}}\\= q^{ \frac{5}{6} . (\frac{-4}{3}) }= q^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ q^{10} }}\\=\frac{1}{q.\sqrt[9]{ q }}=\frac{1}{q.\sqrt[9]{ q }} \color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q^{2}}\\---------------\)
6. \(\left(y^{\frac{1}{3}}\right)^{\frac{-1}{6}}\\= y^{ \frac{1}{3} . (\frac{-1}{6}) }= y^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ y }}=\frac{1}{\sqrt[18]{ y }}. \color{purple}{\frac{\sqrt[18]{ y^{17} }}{\sqrt[18]{ y^{17} }}} \\=\frac{\sqrt[18]{ y^{17} }}{|y|}\\---------------\)
7. \(\left(a^{-1}\right)^{\frac{-1}{3}}\\= a^{ -1 . (\frac{-1}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
8. \(\left(x^{-1}\right)^{\frac{-5}{4}}\\= x^{ -1 . (\frac{-5}{4}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
9. \(\left(y^{\frac{4}{5}}\right)^{1}\\= y^{ \frac{4}{5} . 1 }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
10. \(\left(a^{\frac{-3}{4}}\right)^{-1}\\= a^{ \frac{-3}{4} . (-1) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
11. \(\left(y^{\frac{-2}{3}}\right)^{-1}\\= y^{ \frac{-2}{3} . (-1) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
12. \(\left(y^{\frac{-4}{5}}\right)^{\frac{4}{5}}\\= y^{ \frac{-4}{5} . \frac{4}{5} }= y^{\frac{-16}{25}}\\=\frac{1}{\sqrt[25]{ y^{16} }}=\frac{1}{\sqrt[25]{ y^{16} }}. \color{purple}{\frac{\sqrt[25]{ y^{9} }}{\sqrt[25]{ y^{9} }}} \\=\frac{\sqrt[25]{ y^{9} }}{y}\\---------------\)