Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{5}{4}}\right)^{\frac{-1}{4}}\\= x^{ \frac{5}{4} . (\frac{-1}{4}) }= x^{\frac{-5}{16}}\\=\frac{1}{\sqrt[16]{ x^{5} }}=\frac{1}{\sqrt[16]{ x^{5} }}. \color{purple}{\frac{\sqrt[16]{ x^{11} }}{\sqrt[16]{ x^{11} }}} \\=\frac{\sqrt[16]{ x^{11} }}{|x|}\\---------------\)
2. \(\left(x^{\frac{2}{3}}\right)^{\frac{5}{2}}\\= x^{ \frac{2}{3} . \frac{5}{2} }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
3. \(\left(a^{\frac{-2}{5}}\right)^{-1}\\= a^{ \frac{-2}{5} . (-1) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
4. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-2}{3} . (\frac{-2}{3}) }= a^{\frac{4}{9}}\\=\sqrt[9]{ a^{4} }\\---------------\)
5. \(\left(a^{\frac{-1}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{5} . (\frac{-1}{2}) }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
6. \(\left(y^{\frac{1}{4}}\right)^{\frac{1}{5}}\\= y^{ \frac{1}{4} . \frac{1}{5} }= y^{\frac{1}{20}}\\=\sqrt[20]{ y }\\---------------\)
7. \(\left(q^{\frac{5}{3}}\right)^{-1}\\= q^{ \frac{5}{3} . (-1) }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
8. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-5}{4}}\\= q^{ \frac{-2}{3} . (\frac{-5}{4}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
9. \(\left(a^{\frac{-1}{5}}\right)^{\frac{5}{2}}\\= a^{ \frac{-1}{5} . \frac{5}{2} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
10. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-3}{2}}\\= a^{ \frac{-4}{3} . (\frac{-3}{2}) }= a^{2}\\\\---------------\)
11. \(\left(a^{\frac{-1}{2}}\right)^{1}\\= a^{ \frac{-1}{2} . 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
12. \(\left(q^{\frac{-2}{3}}\right)^{-2}\\= q^{ \frac{-2}{3} . (-2) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)