Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{4}{3}}\right)^{\frac{1}{4}}\\= x^{ \frac{4}{3} . \frac{1}{4} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
2. \(\left(x^{\frac{-4}{5}}\right)^{1}\\= x^{ \frac{-4}{5} . 1 }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
3. \(\left(x^{\frac{-1}{5}}\right)^{-1}\\= x^{ \frac{-1}{5} . (-1) }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
4. \(\left(q^{1}\right)^{\frac{1}{3}}\\= q^{ 1 . \frac{1}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
5. \(\left(y^{-1}\right)^{\frac{1}{2}}\\= y^{ -1 . \frac{1}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
6. \(\left(y^{\frac{5}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{5}{3} . (\frac{-1}{2}) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
7. \(\left(q^{\frac{-1}{5}}\right)^{\frac{1}{2}}\\= q^{ \frac{-1}{5} . \frac{1}{2} }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
8. \(\left(q^{2}\right)^{\frac{-3}{2}}\\= q^{ 2 . (\frac{-3}{2}) }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
9. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-1}{6} . (\frac{-1}{6}) }= q^{\frac{1}{36}}\\=\sqrt[36]{ q }\\---------------\)
10. \(\left(y^{\frac{3}{2}}\right)^{\frac{2}{3}}\\= y^{ \frac{3}{2} . \frac{2}{3} }= y^{1}\\\\---------------\)
11. \(\left(a^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{2}{3} . (\frac{-1}{2}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
12. \(\left(q^{-1}\right)^{1}\\= q^{ -1 . 1 }= q^{-1}\\=\frac{1}{q}\\---------------\)