Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{3}}\\= x^{ \frac{-1}{2} . \frac{1}{3} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
2. \(\left(y^{\frac{3}{5}}\right)^{\frac{-5}{6}}\\= y^{ \frac{3}{5} . (\frac{-5}{6}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
3. \(\left(a^{\frac{1}{4}}\right)^{\frac{1}{3}}\\= a^{ \frac{1}{4} . \frac{1}{3} }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
4. \(\left(a^{\frac{-1}{3}}\right)^{1}\\= a^{ \frac{-1}{3} . 1 }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
5. \(\left(y^{1}\right)^{\frac{1}{6}}\\= y^{ 1 . \frac{1}{6} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
6. \(\left(a^{\frac{-1}{6}}\right)^{\frac{5}{4}}\\= a^{ \frac{-1}{6} . \frac{5}{4} }= a^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ a^{5} }}=\frac{1}{\sqrt[24]{ a^{5} }}. \color{purple}{\frac{\sqrt[24]{ a^{19} }}{\sqrt[24]{ a^{19} }}} \\=\frac{\sqrt[24]{ a^{19} }}{|a|}\\---------------\)
7. \(\left(y^{1}\right)^{\frac{-5}{3}}\\= y^{ 1 . (\frac{-5}{3}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
8. \(\left(y^{\frac{2}{3}}\right)^{-1}\\= y^{ \frac{2}{3} . (-1) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
9. \(\left(x^{\frac{5}{4}}\right)^{1}\\= x^{ \frac{5}{4} . 1 }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
10. \(\left(q^{\frac{-3}{2}}\right)^{2}\\= q^{ \frac{-3}{2} . 2 }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
11. \(\left(x^{-1}\right)^{\frac{-1}{2}}\\= x^{ -1 . (\frac{-1}{2}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
12. \(\left(a^{\frac{3}{4}}\right)^{1}\\= a^{ \frac{3}{4} . 1 }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)