Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{4}{3}}\right)^{-1}\\= q^{ \frac{4}{3} . (-1) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
2. \(\left(y^{\frac{4}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{4}{3} . (\frac{-1}{2}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
3. \(\left(a^{\frac{2}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{2}{3} . \frac{1}{2} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
4. \(\left(x^{2}\right)^{\frac{5}{4}}\\= x^{ 2 . \frac{5}{4} }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
5. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{3}}\\= y^{ \frac{1}{2} . \frac{1}{3} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
6. \(\left(x^{\frac{1}{4}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{4} . \frac{1}{2} }= x^{\frac{1}{8}}\\=\sqrt[8]{ x }\\---------------\)
7. \(\left(y^{\frac{4}{5}}\right)^{\frac{-4}{5}}\\= y^{ \frac{4}{5} . (\frac{-4}{5}) }= y^{\frac{-16}{25}}\\=\frac{1}{\sqrt[25]{ y^{16} }}=\frac{1}{\sqrt[25]{ y^{16} }}. \color{purple}{\frac{\sqrt[25]{ y^{9} }}{\sqrt[25]{ y^{9} }}} \\=\frac{\sqrt[25]{ y^{9} }}{y}\\---------------\)
8. \(\left(q^{\frac{5}{4}}\right)^{-1}\\= q^{ \frac{5}{4} . (-1) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
9. \(\left(y^{\frac{-2}{3}}\right)^{\frac{5}{2}}\\= y^{ \frac{-2}{3} . \frac{5}{2} }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
10. \(\left(a^{\frac{-4}{3}}\right)^{-1}\\= a^{ \frac{-4}{3} . (-1) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
11. \(\left(x^{-1}\right)^{\frac{1}{2}}\\= x^{ -1 . \frac{1}{2} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
12. \(\left(q^{\frac{-5}{6}}\right)^{\frac{1}{6}}\\= q^{ \frac{-5}{6} . \frac{1}{6} }= q^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ q^{5} }}=\frac{1}{\sqrt[36]{ q^{5} }}. \color{purple}{\frac{\sqrt[36]{ q^{31} }}{\sqrt[36]{ q^{31} }}} \\=\frac{\sqrt[36]{ q^{31} }}{|q|}\\---------------\)