Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{6}}\right)^{1}\\= y^{ \frac{-1}{6} . 1 }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
2. \(\left(y^{\frac{1}{3}}\right)^{\frac{-1}{4}}\\= y^{ \frac{1}{3} . (\frac{-1}{4}) }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
3. \(\left(q^{\frac{4}{5}}\right)^{\frac{-3}{2}}\\= q^{ \frac{4}{5} . (\frac{-3}{2}) }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)
4. \(\left(a^{\frac{-4}{5}}\right)^{\frac{5}{2}}\\= a^{ \frac{-4}{5} . \frac{5}{2} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
5. \(\left(x^{\frac{4}{5}}\right)^{\frac{-5}{2}}\\= x^{ \frac{4}{5} . (\frac{-5}{2}) }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
6. \(\left(q^{\frac{1}{4}}\right)^{\frac{5}{4}}\\= q^{ \frac{1}{4} . \frac{5}{4} }= q^{\frac{5}{16}}\\=\sqrt[16]{ q^{5} }\\---------------\)
7. \(\left(x^{\frac{-1}{2}}\right)^{\frac{5}{2}}\\= x^{ \frac{-1}{2} . \frac{5}{2} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
8. \(\left(y^{-1}\right)^{\frac{2}{3}}\\= y^{ -1 . \frac{2}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
9. \(\left(x^{\frac{-3}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{-3}{2} . \frac{1}{2} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
10. \(\left(a^{-1}\right)^{\frac{1}{3}}\\= a^{ -1 . \frac{1}{3} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
11. \(\left(a^{\frac{-1}{5}}\right)^{1}\\= a^{ \frac{-1}{5} . 1 }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
12. \(\left(q^{\frac{1}{6}}\right)^{\frac{-1}{4}}\\= q^{ \frac{1}{6} . (\frac{-1}{4}) }= q^{\frac{-1}{24}}\\=\frac{1}{\sqrt[24]{ q }}=\frac{1}{\sqrt[24]{ q }}. \color{purple}{\frac{\sqrt[24]{ q^{23} }}{\sqrt[24]{ q^{23} }}} \\=\frac{\sqrt[24]{ q^{23} }}{|q|}\\---------------\)