Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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