Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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