Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-5}{3}}\right)^{\frac{5}{4}}\\= y^{ \frac{-5}{3} . \frac{5}{4} }= y^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ y^{25} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y }}=\frac{1}{|y^{2}|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{3}|}\\---------------\)
2. \(\left(a^{\frac{-2}{3}}\right)^{-1}\\= a^{ \frac{-2}{3} . (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
3. \(\left(x^{\frac{5}{6}}\right)^{\frac{2}{5}}\\= x^{ \frac{5}{6} . \frac{2}{5} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
4. \(\left(q^{-2}\right)^{\frac{-4}{5}}\\= q^{ -2 . (\frac{-4}{5}) }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)
5. \(\left(x^{\frac{4}{3}}\right)^{2}\\= x^{ \frac{4}{3} . 2 }= x^{\frac{8}{3}}\\=\sqrt[3]{ x^{8} }=x^{2}.\sqrt[3]{ x^{2} }\\---------------\)
6. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-1}{3} . (\frac{-1}{6}) }= a^{\frac{1}{18}}\\=\sqrt[18]{ a }\\---------------\)
7. \(\left(x^{\frac{5}{4}}\right)^{\frac{-5}{6}}\\= x^{ \frac{5}{4} . (\frac{-5}{6}) }= x^{\frac{-25}{24}}\\=\frac{1}{\sqrt[24]{ x^{25} }}\\=\frac{1}{|x|.\sqrt[24]{ x }}=\frac{1}{|x|.\sqrt[24]{ x }} \color{purple}{\frac{\sqrt[24]{ x^{23} }}{\sqrt[24]{ x^{23} }}} \\=\frac{\sqrt[24]{ x^{23} }}{|x^{2}|}\\---------------\)
8. \(\left(q^{\frac{2}{3}}\right)^{\frac{1}{3}}\\= q^{ \frac{2}{3} . \frac{1}{3} }= q^{\frac{2}{9}}\\=\sqrt[9]{ q^{2} }\\---------------\)
9. \(\left(x^{\frac{5}{6}}\right)^{\frac{4}{3}}\\= x^{ \frac{5}{6} . \frac{4}{3} }= x^{\frac{10}{9}}\\=\sqrt[9]{ x^{10} }=x.\sqrt[9]{ x }\\---------------\)
10. \(\left(q^{\frac{-4}{5}}\right)^{\frac{1}{2}}\\= q^{ \frac{-4}{5} . \frac{1}{2} }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
11. \(\left(q^{\frac{-2}{3}}\right)^{\frac{1}{3}}\\= q^{ \frac{-2}{3} . \frac{1}{3} }= q^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ q^{2} }}=\frac{1}{\sqrt[9]{ q^{2} }}. \color{purple}{\frac{\sqrt[9]{ q^{7} }}{\sqrt[9]{ q^{7} }}} \\=\frac{\sqrt[9]{ q^{7} }}{q}\\---------------\)
12. \(\left(y^{\frac{4}{3}}\right)^{\frac{1}{4}}\\= y^{ \frac{4}{3} . \frac{1}{4} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)