Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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