Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-5}{4}}\right)^{\frac{1}{3}}\\= a^{ \frac{-5}{4} . \frac{1}{3} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
2. \(\left(q^{\frac{-1}{5}}\right)^{\frac{-3}{2}}\\= q^{ \frac{-1}{5} . (\frac{-3}{2}) }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
3. \(\left(y^{-1}\right)^{\frac{3}{4}}\\= y^{ -1 . \frac{3}{4} }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
4. \(\left(a^{\frac{-5}{2}}\right)^{\frac{1}{3}}\\= a^{ \frac{-5}{2} . \frac{1}{3} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
5. \(\left(a^{\frac{-5}{4}}\right)^{\frac{3}{4}}\\= a^{ \frac{-5}{4} . \frac{3}{4} }= a^{\frac{-15}{16}}\\=\frac{1}{\sqrt[16]{ a^{15} }}=\frac{1}{\sqrt[16]{ a^{15} }}. \color{purple}{\frac{\sqrt[16]{ a }}{\sqrt[16]{ a }}} \\=\frac{\sqrt[16]{ a }}{|a|}\\---------------\)
6. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-3}{5}}\\= q^{ \frac{-1}{3} . (\frac{-3}{5}) }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
7. \(\left(x^{\frac{1}{6}}\right)^{\frac{5}{6}}\\= x^{ \frac{1}{6} . \frac{5}{6} }= x^{\frac{5}{36}}\\=\sqrt[36]{ x^{5} }\\---------------\)
8. \(\left(x^{\frac{4}{3}}\right)^{\frac{-3}{5}}\\= x^{ \frac{4}{3} . (\frac{-3}{5}) }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
9. \(\left(y^{\frac{-1}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{5} . (\frac{-1}{2}) }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
10. \(\left(a^{\frac{-2}{5}}\right)^{-1}\\= a^{ \frac{-2}{5} . (-1) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
11. \(\left(a^{\frac{2}{3}}\right)^{\frac{5}{4}}\\= a^{ \frac{2}{3} . \frac{5}{4} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
12. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-3}{5}}\\= x^{ \frac{-4}{5} . (\frac{-3}{5}) }= x^{\frac{12}{25}}\\=\sqrt[25]{ x^{12} }\\---------------\)