Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{-1}\right)^{2}\\= y^{ -1 . 2 }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
2. \(\left(y^{\frac{-2}{3}}\right)^{\frac{5}{3}}\\= y^{ \frac{-2}{3} . \frac{5}{3} }= y^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ y^{10} }}\\=\frac{1}{y.\sqrt[9]{ y }}=\frac{1}{y.\sqrt[9]{ y }} \color{purple}{\frac{\sqrt[9]{ y^{8} }}{\sqrt[9]{ y^{8} }}} \\=\frac{\sqrt[9]{ y^{8} }}{y^{2}}\\---------------\)
3. \(\left(q^{\frac{4}{5}}\right)^{\frac{-1}{2}}\\= q^{ \frac{4}{5} . (\frac{-1}{2}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
4. \(\left(y^{\frac{5}{2}}\right)^{\frac{1}{3}}\\= y^{ \frac{5}{2} . \frac{1}{3} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
5. \(\left(a^{1}\right)^{\frac{-5}{6}}\\= a^{ 1 . (\frac{-5}{6}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
6. \(\left(y^{\frac{3}{2}}\right)^{\frac{5}{3}}\\= y^{ \frac{3}{2} . \frac{5}{3} }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
7. \(\left(a^{\frac{2}{3}}\right)^{\frac{-3}{5}}\\= a^{ \frac{2}{3} . (\frac{-3}{5}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
8. \(\left(q^{\frac{5}{4}}\right)^{\frac{3}{2}}\\= q^{ \frac{5}{4} . \frac{3}{2} }= q^{\frac{15}{8}}\\=\sqrt[8]{ q^{15} }=|q|.\sqrt[8]{ q^{7} }\\---------------\)
9. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-4}{3}}\\= y^{ \frac{-1}{3} . (\frac{-4}{3}) }= y^{\frac{4}{9}}\\=\sqrt[9]{ y^{4} }\\---------------\)
10. \(\left(a^{\frac{2}{3}}\right)^{\frac{-5}{6}}\\= a^{ \frac{2}{3} . (\frac{-5}{6}) }= a^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ a^{5} }}=\frac{1}{\sqrt[9]{ a^{5} }}. \color{purple}{\frac{\sqrt[9]{ a^{4} }}{\sqrt[9]{ a^{4} }}} \\=\frac{\sqrt[9]{ a^{4} }}{a}\\---------------\)
11. \(\left(a^{\frac{-5}{6}}\right)^{\frac{1}{3}}\\= a^{ \frac{-5}{6} . \frac{1}{3} }= a^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ a^{5} }}=\frac{1}{\sqrt[18]{ a^{5} }}. \color{purple}{\frac{\sqrt[18]{ a^{13} }}{\sqrt[18]{ a^{13} }}} \\=\frac{\sqrt[18]{ a^{13} }}{|a|}\\---------------\)
12. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-2}{3} . (\frac{-2}{3}) }= a^{\frac{4}{9}}\\=\sqrt[9]{ a^{4} }\\---------------\)