Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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