Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-3}{5}}\right)^{-1}\\= y^{ \frac{-3}{5} . (-1) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
2. \(\left(a^{\frac{2}{5}}\right)^{\frac{4}{3}}\\= a^{ \frac{2}{5} . \frac{4}{3} }= a^{\frac{8}{15}}\\=\sqrt[15]{ a^{8} }\\---------------\)
3. \(\left(x^{\frac{-1}{4}}\right)^{\frac{4}{3}}\\= x^{ \frac{-1}{4} . \frac{4}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
4. \(\left(q^{\frac{3}{4}}\right)^{\frac{-3}{2}}\\= q^{ \frac{3}{4} . (\frac{-3}{2}) }= q^{\frac{-9}{8}}\\=\frac{1}{\sqrt[8]{ q^{9} }}\\=\frac{1}{|q|.\sqrt[8]{ q }}=\frac{1}{|q|.\sqrt[8]{ q }} \color{purple}{\frac{\sqrt[8]{ q^{7} }}{\sqrt[8]{ q^{7} }}} \\=\frac{\sqrt[8]{ q^{7} }}{|q^{2}|}\\---------------\)
5. \(\left(a^{\frac{-1}{2}}\right)^{\frac{4}{5}}\\= a^{ \frac{-1}{2} . \frac{4}{5} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
6. \(\left(a^{-1}\right)^{-1}\\= a^{ -1 . (-1) }= a^{1}\\\\---------------\)
7. \(\left(a^{-1}\right)^{\frac{-4}{5}}\\= a^{ -1 . (\frac{-4}{5}) }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
8. \(\left(x^{1}\right)^{-1}\\= x^{ 1 . (-1) }= x^{-1}\\=\frac{1}{x}\\---------------\)
9. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-5}{2}}\\= x^{ \frac{-4}{5} . (\frac{-5}{2}) }= x^{2}\\\\---------------\)
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. \(\left(q^{\frac{-1}{4}}\right)^{\frac{5}{6}}\\= q^{ \frac{-1}{4} . \frac{5}{6} }= q^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ q^{5} }}=\frac{1}{\sqrt[24]{ q^{5} }}. \color{purple}{\frac{\sqrt[24]{ q^{19} }}{\sqrt[24]{ q^{19} }}} \\=\frac{\sqrt[24]{ q^{19} }}{|q|}\\---------------\)
12. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-1}{6} . (\frac{-1}{2}) }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)