Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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