Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-2}{3}}\right)^{1}\\= y^{ \frac{-2}{3} . 1 }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
2. \(\left(y^{\frac{-5}{2}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-5}{2} . (\frac{-5}{6}) }= y^{\frac{25}{12}}\\=\sqrt[12]{ y^{25} }=|y^{2}|.\sqrt[12]{ y }\\---------------\)
3. \(\left(q^{\frac{-3}{4}}\right)^{1}\\= q^{ \frac{-3}{4} . 1 }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
4. \(\left(q^{\frac{-1}{4}}\right)^{\frac{-4}{3}}\\= q^{ \frac{-1}{4} . (\frac{-4}{3}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
5. \(\left(a^{2}\right)^{\frac{5}{2}}\\= a^{ 2 . \frac{5}{2} }= a^{5}\\\\---------------\)
6. \(\left(y^{\frac{5}{2}}\right)^{1}\\= y^{ \frac{5}{2} . 1 }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
7. \(\left(y^{\frac{1}{3}}\right)^{\frac{5}{4}}\\= y^{ \frac{1}{3} . \frac{5}{4} }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
8. \(\left(y^{\frac{1}{3}}\right)^{\frac{-5}{6}}\\= y^{ \frac{1}{3} . (\frac{-5}{6}) }= y^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ y^{5} }}=\frac{1}{\sqrt[18]{ y^{5} }}. \color{purple}{\frac{\sqrt[18]{ y^{13} }}{\sqrt[18]{ y^{13} }}} \\=\frac{\sqrt[18]{ y^{13} }}{|y|}\\---------------\)
9. \(\left(y^{\frac{-3}{5}}\right)^{\frac{-1}{5}}\\= y^{ \frac{-3}{5} . (\frac{-1}{5}) }= y^{\frac{3}{25}}\\=\sqrt[25]{ y^{3} }\\---------------\)
10. \(\left(x^{\frac{-1}{4}}\right)^{\frac{2}{3}}\\= x^{ \frac{-1}{4} . \frac{2}{3} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
11. \(\left(x^{-1}\right)^{\frac{1}{4}}\\= x^{ -1 . \frac{1}{4} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
12. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-1}{3} . (\frac{-4}{3}) }= a^{\frac{4}{9}}\\=\sqrt[9]{ a^{4} }\\---------------\)