Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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