Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-5}{2}}\right)^{\frac{-5}{3}}\\= y^{ \frac{-5}{2} . (\frac{-5}{3}) }= y^{\frac{25}{6}}\\=\sqrt[6]{ y^{25} }=|y^{4}|.\sqrt[6]{ y }\\---------------\)
2. \(\left(q^{\frac{3}{5}}\right)^{\frac{2}{3}}\\= q^{ \frac{3}{5} . \frac{2}{3} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
3. \(\left(a^{\frac{-5}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-5}{3} . (\frac{-2}{3}) }= a^{\frac{10}{9}}\\=\sqrt[9]{ a^{10} }=a.\sqrt[9]{ a }\\---------------\)
4. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{2} . \frac{1}{2} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
5. \(\left(y^{\frac{1}{2}}\right)^{\frac{-1}{3}}\\= y^{ \frac{1}{2} . (\frac{-1}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
6. \(\left(y^{\frac{3}{4}}\right)^{\frac{-1}{2}}\\= y^{ \frac{3}{4} . (\frac{-1}{2}) }= y^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ y^{3} }}=\frac{1}{\sqrt[8]{ y^{3} }}. \color{purple}{\frac{\sqrt[8]{ y^{5} }}{\sqrt[8]{ y^{5} }}} \\=\frac{\sqrt[8]{ y^{5} }}{|y|}\\---------------\)
7. \(\left(q^{\frac{3}{5}}\right)^{\frac{-2}{3}}\\= q^{ \frac{3}{5} . (\frac{-2}{3}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
8. \(\left(a^{\frac{-3}{4}}\right)^{\frac{1}{6}}\\= a^{ \frac{-3}{4} . \frac{1}{6} }= a^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ a }}=\frac{1}{\sqrt[8]{ a }}. \color{purple}{\frac{\sqrt[8]{ a^{7} }}{\sqrt[8]{ a^{7} }}} \\=\frac{\sqrt[8]{ a^{7} }}{|a|}\\---------------\)
9. \(\left(q^{\frac{-3}{5}}\right)^{\frac{-1}{4}}\\= q^{ \frac{-3}{5} . (\frac{-1}{4}) }= q^{\frac{3}{20}}\\=\sqrt[20]{ q^{3} }\\---------------\)
10. \(\left(a^{\frac{-3}{5}}\right)^{2}\\= a^{ \frac{-3}{5} . 2 }= a^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ a^{6} }}\\=\frac{1}{a.\sqrt[5]{ a }}=\frac{1}{a.\sqrt[5]{ a }} \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a^{2}}\\---------------\)
11. \(\left(a^{\frac{-2}{5}}\right)^{-1}\\= a^{ \frac{-2}{5} . (-1) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
12. \(\left(x^{-1}\right)^{\frac{1}{2}}\\= x^{ -1 . \frac{1}{2} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)