Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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