Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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