Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{2}}\right)^{-1}\\= y^{ \frac{1}{2} . (-1) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
2. \(\left(a^{\frac{-4}{3}}\right)^{1}\\= a^{ \frac{-4}{3} . 1 }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
3. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-5}{2}}\\= a^{ \frac{-1}{2} . (\frac{-5}{2}) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
4. \(\left(y^{\frac{-1}{2}}\right)^{\frac{3}{4}}\\= y^{ \frac{-1}{2} . \frac{3}{4} }= y^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ y^{3} }}=\frac{1}{\sqrt[8]{ y^{3} }}. \color{purple}{\frac{\sqrt[8]{ y^{5} }}{\sqrt[8]{ y^{5} }}} \\=\frac{\sqrt[8]{ y^{5} }}{|y|}\\---------------\)
5. \(\left(y^{\frac{1}{4}}\right)^{-1}\\= y^{ \frac{1}{4} . (-1) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
6. \(\left(q^{-2}\right)^{-1}\\= q^{ -2 . (-1) }= q^{2}\\\\---------------\)
7. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-3}{2}}\\= y^{ \frac{-2}{5} . (\frac{-3}{2}) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
8. \(\left(x^{\frac{4}{5}}\right)^{1}\\= x^{ \frac{4}{5} . 1 }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)
9. \(\left(y^{-1}\right)^{\frac{4}{3}}\\= y^{ -1 . \frac{4}{3} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
10. \(\left(q^{\frac{-1}{5}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-1}{5} . (\frac{-1}{6}) }= q^{\frac{1}{30}}\\=\sqrt[30]{ q }\\---------------\)
11. \(\left(a^{1}\right)^{\frac{-1}{2}}\\= a^{ 1 . (\frac{-1}{2}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
12. \(\left(a^{\frac{5}{2}}\right)^{1}\\= a^{ \frac{5}{2} . 1 }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)