Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{3}}\right)^{\frac{1}{3}}\\= x^{ \frac{-1}{3} . \frac{1}{3} }= x^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ x }}=\frac{1}{\sqrt[9]{ x }}. \color{purple}{\frac{\sqrt[9]{ x^{8} }}{\sqrt[9]{ x^{8} }}} \\=\frac{\sqrt[9]{ x^{8} }}{x}\\---------------\)
2. \(\left(x^{-1}\right)^{\frac{-2}{3}}\\= x^{ -1 . (\frac{-2}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
3. \(\left(x^{\frac{3}{2}}\right)^{\frac{-1}{3}}\\= x^{ \frac{3}{2} . (\frac{-1}{3}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
4. \(\left(a^{\frac{-3}{2}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-3}{2} . (\frac{-1}{3}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
5. \(\left(a^{\frac{-2}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{-2}{3} . \frac{1}{2} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
6. \(\left(a^{\frac{-1}{2}}\right)^{-2}\\= a^{ \frac{-1}{2} . (-2) }= a^{1}\\\\---------------\)
7. \(\left(a^{\frac{-1}{2}}\right)^{2}\\= a^{ \frac{-1}{2} . 2 }= a^{-1}\\=\frac{1}{a}\\---------------\)
8. \(\left(y^{\frac{4}{3}}\right)^{\frac{-1}{5}}\\= y^{ \frac{4}{3} . (\frac{-1}{5}) }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
9. \(\left(x^{\frac{3}{4}}\right)^{\frac{-3}{4}}\\= x^{ \frac{3}{4} . (\frac{-3}{4}) }= x^{\frac{-9}{16}}\\=\frac{1}{\sqrt[16]{ x^{9} }}=\frac{1}{\sqrt[16]{ x^{9} }}. \color{purple}{\frac{\sqrt[16]{ x^{7} }}{\sqrt[16]{ x^{7} }}} \\=\frac{\sqrt[16]{ x^{7} }}{|x|}\\---------------\)
10. \(\left(x^{1}\right)^{\frac{1}{6}}\\= x^{ 1 . \frac{1}{6} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
11. \(\left(q^{\frac{-3}{4}}\right)^{-1}\\= q^{ \frac{-3}{4} . (-1) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
12. \(\left(a^{\frac{-5}{2}}\right)^{\frac{4}{3}}\\= a^{ \frac{-5}{2} . \frac{4}{3} }= a^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ a^{10} }}\\=\frac{1}{a^{3}.\sqrt[3]{ a }}=\frac{1}{a^{3}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{4}}\\---------------\)