Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{1}\right)^{-1}\\= y^{ 1 . (-1) }= y^{-1}\\=\frac{1}{y}\\---------------\)
2. \(\left(x^{-1}\right)^{\frac{-3}{4}}\\= x^{ -1 . (\frac{-3}{4}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
3. \(\left(q^{\frac{-1}{2}}\right)^{\frac{4}{5}}\\= q^{ \frac{-1}{2} . \frac{4}{5} }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
4. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-1}{3} . (\frac{-1}{6}) }= a^{\frac{1}{18}}\\=\sqrt[18]{ a }\\---------------\)
5. \(\left(a^{\frac{-1}{5}}\right)^{\frac{5}{4}}\\= a^{ \frac{-1}{5} . \frac{5}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
6. \(\left(a^{\frac{1}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{1}{3} . \frac{1}{2} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
7. \(\left(q^{\frac{-3}{4}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-3}{4} . (\frac{-1}{2}) }= q^{\frac{3}{8}}\\=\sqrt[8]{ q^{3} }\\---------------\)
8. \(\left(a^{\frac{3}{4}}\right)^{1}\\= a^{ \frac{3}{4} . 1 }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
9. \(\left(x^{\frac{-2}{3}}\right)^{\frac{2}{3}}\\= x^{ \frac{-2}{3} . \frac{2}{3} }= x^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ x^{4} }}=\frac{1}{\sqrt[9]{ x^{4} }}. \color{purple}{\frac{\sqrt[9]{ x^{5} }}{\sqrt[9]{ x^{5} }}} \\=\frac{\sqrt[9]{ x^{5} }}{x}\\---------------\)
10. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-1}{3}}\\= x^{ \frac{-1}{2} . (\frac{-1}{3}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
11. \(\left(x^{1}\right)^{\frac{4}{5}}\\= x^{ 1 . \frac{4}{5} }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)
12. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-5}{4}}\\= x^{ \frac{-2}{3} . (\frac{-5}{4}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)