Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{3}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{3} . (\frac{-1}{3}) }= q^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ q }}=\frac{1}{\sqrt[9]{ q }}. \color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q}\\---------------\)
2. \(\left(x^{\frac{1}{6}}\right)^{\frac{2}{3}}\\= x^{ \frac{1}{6} . \frac{2}{3} }= x^{\frac{1}{9}}\\=\sqrt[9]{ x }\\---------------\)
3. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-1}{4}}\\= y^{ \frac{-1}{3} . (\frac{-1}{4}) }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
4. \(\left(y^{\frac{5}{2}}\right)^{\frac{-2}{3}}\\= y^{ \frac{5}{2} . (\frac{-2}{3}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
5. \(\left(q^{1}\right)^{\frac{1}{2}}\\= q^{ 1 . \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
6. \(\left(a^{\frac{-1}{3}}\right)^{\frac{3}{2}}\\= a^{ \frac{-1}{3} . \frac{3}{2} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
7. \(\left(q^{2}\right)^{\frac{-3}{2}}\\= q^{ 2 . (\frac{-3}{2}) }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
8. \(\left(a^{\frac{3}{5}}\right)^{\frac{-2}{3}}\\= a^{ \frac{3}{5} . (\frac{-2}{3}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
9. \(\left(a^{\frac{-4}{5}}\right)^{\frac{-5}{3}}\\= a^{ \frac{-4}{5} . (\frac{-5}{3}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
10. \(\left(y^{\frac{1}{3}}\right)^{\frac{1}{2}}\\= y^{ \frac{1}{3} . \frac{1}{2} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
11. \(\left(y^{\frac{3}{5}}\right)^{\frac{-1}{4}}\\= y^{ \frac{3}{5} . (\frac{-1}{4}) }= y^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ y^{3} }}=\frac{1}{\sqrt[20]{ y^{3} }}. \color{purple}{\frac{\sqrt[20]{ y^{17} }}{\sqrt[20]{ y^{17} }}} \\=\frac{\sqrt[20]{ y^{17} }}{|y|}\\---------------\)
12. \(\left(q^{\frac{4}{5}}\right)^{\frac{-5}{2}}\\= q^{ \frac{4}{5} . (\frac{-5}{2}) }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)