Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-2}{5}}\right)^{\frac{1}{5}}\\= a^{ \frac{-2}{5} . \frac{1}{5} }= a^{\frac{-2}{25}}\\=\frac{1}{\sqrt[25]{ a^{2} }}=\frac{1}{\sqrt[25]{ a^{2} }}. \color{purple}{\frac{\sqrt[25]{ a^{23} }}{\sqrt[25]{ a^{23} }}} \\=\frac{\sqrt[25]{ a^{23} }}{a}\\---------------\)
2. \(\left(a^{1}\right)^{\frac{2}{5}}\\= a^{ 1 . \frac{2}{5} }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
3. \(\left(q^{\frac{3}{5}}\right)^{-1}\\= q^{ \frac{3}{5} . (-1) }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
4. \(\left(a^{\frac{1}{2}}\right)^{\frac{-3}{5}}\\= a^{ \frac{1}{2} . (\frac{-3}{5}) }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
5. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-1}{3} . (\frac{-1}{2}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
6. \(\left(a^{1}\right)^{\frac{-2}{3}}\\= a^{ 1 . (\frac{-2}{3}) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
7. \(\left(y^{\frac{4}{3}}\right)^{-1}\\= y^{ \frac{4}{3} . (-1) }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
8. \(\left(a^{\frac{-1}{2}}\right)^{\frac{5}{6}}\\= a^{ \frac{-1}{2} . \frac{5}{6} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
9. \(\left(q^{\frac{-1}{2}}\right)^{\frac{1}{3}}\\= q^{ \frac{-1}{2} . \frac{1}{3} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
10. \(\left(y^{\frac{-5}{3}}\right)^{\frac{2}{5}}\\= y^{ \frac{-5}{3} . \frac{2}{5} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
11. \(\left(a^{\frac{-5}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{-5}{3} . \frac{1}{2} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
12. \(\left(y^{\frac{3}{5}}\right)^{\frac{2}{3}}\\= y^{ \frac{3}{5} . \frac{2}{3} }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)