Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{1}\right)^{\frac{1}{6}}\\= q^{ 1 . \frac{1}{6} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
2. \(\left(a^{\frac{3}{4}}\right)^{\frac{3}{4}}\\= a^{ \frac{3}{4} . \frac{3}{4} }= a^{\frac{9}{16}}\\=\sqrt[16]{ a^{9} }\\---------------\)
3. \(\left(x^{\frac{3}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{3}{5} . \frac{1}{2} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
4. \(\left(y^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{1}{3} . (\frac{-1}{2}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
5. \(\left(x^{1}\right)^{-1}\\= x^{ 1 . (-1) }= x^{-1}\\=\frac{1}{x}\\---------------\)
6. \(\left(a^{\frac{-1}{2}}\right)^{-1}\\= a^{ \frac{-1}{2} . (-1) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
7. \(\left(a^{\frac{2}{5}}\right)^{\frac{2}{3}}\\= a^{ \frac{2}{5} . \frac{2}{3} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
8. \(\left(x^{2}\right)^{\frac{1}{2}}\\= x^{ 2 . \frac{1}{2} }= x^{1}\\\\---------------\)
9. \(\left(y^{2}\right)^{\frac{-3}{2}}\\= y^{ 2 . (\frac{-3}{2}) }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
10. \(\left(a^{\frac{5}{6}}\right)^{\frac{-2}{5}}\\= a^{ \frac{5}{6} . (\frac{-2}{5}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
11. \(\left(q^{\frac{1}{3}}\right)^{\frac{-1}{6}}\\= q^{ \frac{1}{3} . (\frac{-1}{6}) }= q^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ q }}=\frac{1}{\sqrt[18]{ q }}. \color{purple}{\frac{\sqrt[18]{ q^{17} }}{\sqrt[18]{ q^{17} }}} \\=\frac{\sqrt[18]{ q^{17} }}{|q|}\\---------------\)
12. \(\left(x^{\frac{-5}{2}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-5}{2} . (\frac{-2}{3}) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)