Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{-1}\right)^{\frac{-3}{2}}\\= y^{ -1 . (\frac{-3}{2}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
2. \(\left(y^{\frac{5}{6}}\right)^{\frac{5}{6}}\\= y^{ \frac{5}{6} . \frac{5}{6} }= y^{\frac{25}{36}}\\=\sqrt[36]{ y^{25} }\\---------------\)
3. \(\left(q^{\frac{-5}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{-5}{2} . \frac{1}{2} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
4. \(\left(q^{\frac{5}{6}}\right)^{-1}\\= q^{ \frac{5}{6} . (-1) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
5. \(\left(x^{\frac{-4}{3}}\right)^{\frac{5}{3}}\\= x^{ \frac{-4}{3} . \frac{5}{3} }= x^{\frac{-20}{9}}\\=\frac{1}{\sqrt[9]{ x^{20} }}\\=\frac{1}{x^{2}.\sqrt[9]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[9]{ x^{2} }} \color{purple}{\frac{\sqrt[9]{ x^{7} }}{\sqrt[9]{ x^{7} }}} \\=\frac{\sqrt[9]{ x^{7} }}{x^{3}}\\---------------\)
6. \(\left(x^{\frac{-1}{2}}\right)^{\frac{4}{3}}\\= x^{ \frac{-1}{2} . \frac{4}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
7. \(\left(y^{\frac{-4}{5}}\right)^{\frac{-5}{2}}\\= y^{ \frac{-4}{5} . (\frac{-5}{2}) }= y^{2}\\\\---------------\)
8. \(\left(q^{2}\right)^{\frac{-3}{4}}\\= q^{ 2 . (\frac{-3}{4}) }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
9. \(\left(a^{\frac{-5}{6}}\right)^{-1}\\= a^{ \frac{-5}{6} . (-1) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
10. \(\left(y^{\frac{-3}{4}}\right)^{\frac{5}{4}}\\= y^{ \frac{-3}{4} . \frac{5}{4} }= y^{\frac{-15}{16}}\\=\frac{1}{\sqrt[16]{ y^{15} }}=\frac{1}{\sqrt[16]{ y^{15} }}. \color{purple}{\frac{\sqrt[16]{ y }}{\sqrt[16]{ y }}} \\=\frac{\sqrt[16]{ y }}{|y|}\\---------------\)
11. \(\left(y^{\frac{-5}{6}}\right)^{\frac{5}{3}}\\= y^{ \frac{-5}{6} . \frac{5}{3} }= y^{\frac{-25}{18}}\\=\frac{1}{\sqrt[18]{ y^{25} }}\\=\frac{1}{|y|.\sqrt[18]{ y^{7} }}=\frac{1}{|y|.\sqrt[18]{ y^{7} }} \color{purple}{\frac{\sqrt[18]{ y^{11} }}{\sqrt[18]{ y^{11} }}} \\=\frac{\sqrt[18]{ y^{11} }}{|y^{2}|}\\---------------\)
12. \(\left(y^{\frac{2}{3}}\right)^{\frac{-1}{3}}\\= y^{ \frac{2}{3} . (\frac{-1}{3}) }= y^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ y^{2} }}=\frac{1}{\sqrt[9]{ y^{2} }}. \color{purple}{\frac{\sqrt[9]{ y^{7} }}{\sqrt[9]{ y^{7} }}} \\=\frac{\sqrt[9]{ y^{7} }}{y}\\---------------\)