Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-2}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{-2}{3} . \frac{1}{2} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
2. \(\left(q^{\frac{-1}{2}}\right)^{1}\\= q^{ \frac{-1}{2} . 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
3. \(\left(a^{\frac{3}{2}}\right)^{\frac{5}{2}}\\= a^{ \frac{3}{2} . \frac{5}{2} }= a^{\frac{15}{4}}\\=\sqrt[4]{ a^{15} }=|a^{3}|.\sqrt[4]{ a^{3} }\\---------------\)
4. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-4}{5}}\\= a^{ \frac{-1}{3} . (\frac{-4}{5}) }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
5. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-1}{3} . (\frac{-1}{3}) }= a^{\frac{1}{9}}\\=\sqrt[9]{ a }\\---------------\)
6. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-1}{4}}\\= y^{ \frac{-1}{2} . (\frac{-1}{4}) }= y^{\frac{1}{8}}\\=\sqrt[8]{ y }\\---------------\)
7. \(\left(a^{-1}\right)^{\frac{-4}{5}}\\= a^{ -1 . (\frac{-4}{5}) }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
8. \(\left(y^{\frac{2}{3}}\right)^{\frac{-4}{3}}\\= y^{ \frac{2}{3} . (\frac{-4}{3}) }= y^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ y^{8} }}=\frac{1}{\sqrt[9]{ y^{8} }}. \color{purple}{\frac{\sqrt[9]{ y }}{\sqrt[9]{ y }}} \\=\frac{\sqrt[9]{ y }}{y}\\---------------\)
9. \(\left(q^{\frac{-5}{3}}\right)^{\frac{-1}{4}}\\= q^{ \frac{-5}{3} . (\frac{-1}{4}) }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
10. \(\left(y^{\frac{5}{2}}\right)^{\frac{-1}{5}}\\= y^{ \frac{5}{2} . (\frac{-1}{5}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
11. \(\left(q^{\frac{1}{2}}\right)^{\frac{-4}{3}}\\= q^{ \frac{1}{2} . (\frac{-4}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
12. \(\left(y^{\frac{1}{4}}\right)^{\frac{-2}{5}}\\= y^{ \frac{1}{4} . (\frac{-2}{5}) }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)