Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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