Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{5}{2}}\right)^{\frac{3}{2}}\\= x^{ \frac{5}{2} . \frac{3}{2} }= x^{\frac{15}{4}}\\=\sqrt[4]{ x^{15} }=|x^{3}|.\sqrt[4]{ x^{3} }\\---------------\)
2. \(\left(x^{\frac{-4}{3}}\right)^{\frac{2}{3}}\\= x^{ \frac{-4}{3} . \frac{2}{3} }= x^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ x^{8} }}=\frac{1}{\sqrt[9]{ x^{8} }}. \color{purple}{\frac{\sqrt[9]{ x }}{\sqrt[9]{ x }}} \\=\frac{\sqrt[9]{ x }}{x}\\---------------\)
3. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-1}{3} . (\frac{-1}{3}) }= q^{\frac{1}{9}}\\=\sqrt[9]{ q }\\---------------\)
4. \(\left(x^{\frac{4}{3}}\right)^{\frac{1}{6}}\\= x^{ \frac{4}{3} . \frac{1}{6} }= x^{\frac{2}{9}}\\=\sqrt[9]{ x^{2} }\\---------------\)
5. \(\left(x^{\frac{-1}{2}}\right)^{\frac{3}{2}}\\= x^{ \frac{-1}{2} . \frac{3}{2} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
6. \(\left(x^{\frac{1}{2}}\right)^{\frac{-3}{2}}\\= x^{ \frac{1}{2} . (\frac{-3}{2}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
7. \(\left(a^{\frac{4}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{4}{3} . \frac{2}{3} }= a^{\frac{8}{9}}\\=\sqrt[9]{ a^{8} }\\---------------\)
8. \(\left(a^{\frac{5}{6}}\right)^{\frac{-3}{5}}\\= a^{ \frac{5}{6} . (\frac{-3}{5}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
9. \(\left(y^{\frac{2}{5}}\right)^{\frac{2}{5}}\\= y^{ \frac{2}{5} . \frac{2}{5} }= y^{\frac{4}{25}}\\=\sqrt[25]{ y^{4} }\\---------------\)
10. \(\left(y^{1}\right)^{\frac{3}{2}}\\= y^{ 1 . \frac{3}{2} }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
11. \(\left(y^{\frac{1}{4}}\right)^{2}\\= y^{ \frac{1}{4} . 2 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
12. \(\left(a^{\frac{-2}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{-2}{3} . \frac{1}{3} }= a^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ a^{2} }}=\frac{1}{\sqrt[9]{ a^{2} }}. \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a}\\---------------\)