Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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