Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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