Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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