Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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