Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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