Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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