Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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