Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{5}}\right)^{\frac{-3}{4}}\\= x^{ \frac{1}{5} . (\frac{-3}{4}) }= x^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ x^{3} }}=\frac{1}{\sqrt[20]{ x^{3} }}. \color{purple}{\frac{\sqrt[20]{ x^{17} }}{\sqrt[20]{ x^{17} }}} \\=\frac{\sqrt[20]{ x^{17} }}{|x|}\\---------------\)
2. \(\left(a^{\frac{4}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{4}{3} . (\frac{-2}{3}) }= a^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ a^{8} }}=\frac{1}{\sqrt[9]{ a^{8} }}. \color{purple}{\frac{\sqrt[9]{ a }}{\sqrt[9]{ a }}} \\=\frac{\sqrt[9]{ a }}{a}\\---------------\)
3. \(\left(q^{\frac{1}{3}}\right)^{\frac{5}{4}}\\= q^{ \frac{1}{3} . \frac{5}{4} }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
4. \(\left(a^{\frac{1}{2}}\right)^{\frac{3}{2}}\\= a^{ \frac{1}{2} . \frac{3}{2} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
5. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{1}{2} . \frac{1}{2} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
6. \(\left(a^{\frac{-5}{3}}\right)^{-1}\\= a^{ \frac{-5}{3} . (-1) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
7. \(\left(q^{\frac{-2}{5}}\right)^{\frac{-3}{2}}\\= q^{ \frac{-2}{5} . (\frac{-3}{2}) }= q^{\frac{3}{5}}\\=\sqrt[5]{ q^{3} }\\---------------\)
8. \(\left(y^{\frac{-1}{4}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{4} . (\frac{-1}{2}) }= y^{\frac{1}{8}}\\=\sqrt[8]{ y }\\---------------\)
9. \(\left(a^{\frac{-5}{6}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-5}{6} . (\frac{-4}{3}) }= a^{\frac{10}{9}}\\=\sqrt[9]{ a^{10} }=a.\sqrt[9]{ a }\\---------------\)
10. \(\left(y^{\frac{-5}{3}}\right)^{\frac{-3}{2}}\\= y^{ \frac{-5}{3} . (\frac{-3}{2}) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
11. \(\left(y^{\frac{-5}{3}}\right)^{\frac{1}{5}}\\= y^{ \frac{-5}{3} . \frac{1}{5} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
12. \(\left(a^{\frac{1}{4}}\right)^{\frac{5}{2}}\\= a^{ \frac{1}{4} . \frac{5}{2} }= a^{\frac{5}{8}}\\=\sqrt[8]{ a^{5} }\\---------------\)