Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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