Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-3}{4}}\right)^{\frac{1}{2}}\\= q^{ \frac{-3}{4} . \frac{1}{2} }= q^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ q^{3} }}=\frac{1}{\sqrt[8]{ q^{3} }}. \color{purple}{\frac{\sqrt[8]{ q^{5} }}{\sqrt[8]{ q^{5} }}} \\=\frac{\sqrt[8]{ q^{5} }}{|q|}\\---------------\)
2. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-2}{5}}\\= x^{ \frac{-4}{5} . (\frac{-2}{5}) }= x^{\frac{8}{25}}\\=\sqrt[25]{ x^{8} }\\---------------\)
3. \(\left(a^{1}\right)^{-1}\\= a^{ 1 . (-1) }= a^{-1}\\=\frac{1}{a}\\---------------\)
4. \(\left(y^{\frac{2}{3}}\right)^{\frac{4}{5}}\\= y^{ \frac{2}{3} . \frac{4}{5} }= y^{\frac{8}{15}}\\=\sqrt[15]{ y^{8} }\\---------------\)
5. \(\left(y^{\frac{-3}{5}}\right)^{\frac{1}{6}}\\= y^{ \frac{-3}{5} . \frac{1}{6} }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
6. \(\left(x^{\frac{-2}{5}}\right)^{\frac{2}{5}}\\= x^{ \frac{-2}{5} . \frac{2}{5} }= x^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ x^{4} }}=\frac{1}{\sqrt[25]{ x^{4} }}. \color{purple}{\frac{\sqrt[25]{ x^{21} }}{\sqrt[25]{ x^{21} }}} \\=\frac{\sqrt[25]{ x^{21} }}{x}\\---------------\)
7. \(\left(y^{\frac{-1}{6}}\right)^{\frac{-4}{3}}\\= y^{ \frac{-1}{6} . (\frac{-4}{3}) }= y^{\frac{2}{9}}\\=\sqrt[9]{ y^{2} }\\---------------\)
8. \(\left(x^{\frac{5}{4}}\right)^{\frac{-1}{3}}\\= x^{ \frac{5}{4} . (\frac{-1}{3}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
9. \(\left(a^{\frac{-5}{2}}\right)^{\frac{2}{3}}\\= a^{ \frac{-5}{2} . \frac{2}{3} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
10. \(\left(x^{\frac{-5}{6}}\right)^{\frac{-3}{2}}\\= x^{ \frac{-5}{6} . (\frac{-3}{2}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
11. \(\left(a^{\frac{5}{3}}\right)^{\frac{-1}{3}}\\= a^{ \frac{5}{3} . (\frac{-1}{3}) }= a^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ a^{5} }}=\frac{1}{\sqrt[9]{ a^{5} }}. \color{purple}{\frac{\sqrt[9]{ a^{4} }}{\sqrt[9]{ a^{4} }}} \\=\frac{\sqrt[9]{ a^{4} }}{a}\\---------------\)
12. \(\left(y^{\frac{1}{2}}\right)^{\frac{-1}{3}}\\= y^{ \frac{1}{2} . (\frac{-1}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)