Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{2}{3} . (\frac{-1}{2}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
2. \(\left(x^{\frac{4}{3}}\right)^{\frac{1}{4}}\\= x^{ \frac{4}{3} . \frac{1}{4} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
3. \(\left(q^{\frac{2}{3}}\right)^{\frac{2}{3}}\\= q^{ \frac{2}{3} . \frac{2}{3} }= q^{\frac{4}{9}}\\=\sqrt[9]{ q^{4} }\\---------------\)
4. \(\left(x^{\frac{2}{3}}\right)^{\frac{5}{6}}\\= x^{ \frac{2}{3} . \frac{5}{6} }= x^{\frac{5}{9}}\\=\sqrt[9]{ x^{5} }\\---------------\)
5. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-1}{5}}\\= y^{ \frac{-1}{2} . (\frac{-1}{5}) }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
6. \(\left(q^{\frac{-2}{3}}\right)^{\frac{5}{3}}\\= q^{ \frac{-2}{3} . \frac{5}{3} }= q^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ q^{10} }}\\=\frac{1}{q.\sqrt[9]{ q }}=\frac{1}{q.\sqrt[9]{ q }} \color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q^{2}}\\---------------\)
7. \(\left(x^{\frac{1}{5}}\right)^{\frac{-2}{3}}\\= x^{ \frac{1}{5} . (\frac{-2}{3}) }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
8. \(\left(x^{-1}\right)^{1}\\= x^{ -1 . 1 }= x^{-1}\\=\frac{1}{x}\\---------------\)
9. \(\left(y^{\frac{-5}{3}}\right)^{\frac{-4}{5}}\\= y^{ \frac{-5}{3} . (\frac{-4}{5}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
10. \(\left(q^{\frac{1}{6}}\right)^{\frac{2}{3}}\\= q^{ \frac{1}{6} . \frac{2}{3} }= q^{\frac{1}{9}}\\=\sqrt[9]{ q }\\---------------\)
11. \(\left(y^{\frac{-5}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-5}{3} . (\frac{-1}{2}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
12. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-2}{3} . (\frac{-1}{2}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)