Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{4}{5}}\right)^{1}\\= q^{ \frac{4}{5} . 1 }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
2. \(\left(y^{\frac{1}{6}}\right)^{\frac{-1}{4}}\\= y^{ \frac{1}{6} . (\frac{-1}{4}) }= y^{\frac{-1}{24}}\\=\frac{1}{\sqrt[24]{ y }}=\frac{1}{\sqrt[24]{ y }}. \color{purple}{\frac{\sqrt[24]{ y^{23} }}{\sqrt[24]{ y^{23} }}} \\=\frac{\sqrt[24]{ y^{23} }}{|y|}\\---------------\)
3. \(\left(x^{\frac{-1}{3}}\right)^{1}\\= x^{ \frac{-1}{3} . 1 }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
4. \(\left(y^{1}\right)^{\frac{1}{3}}\\= y^{ 1 . \frac{1}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
5. \(\left(q^{\frac{-1}{2}}\right)^{\frac{4}{3}}\\= q^{ \frac{-1}{2} . \frac{4}{3} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
6. \(\left(x^{\frac{2}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{2}{5} . (\frac{-1}{2}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
7. \(\left(a^{-1}\right)^{\frac{5}{3}}\\= a^{ -1 . \frac{5}{3} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
8. \(\left(q^{\frac{1}{6}}\right)^{\frac{3}{5}}\\= q^{ \frac{1}{6} . \frac{3}{5} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
9. \(\left(x^{-1}\right)^{\frac{5}{6}}\\= x^{ -1 . \frac{5}{6} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
10. \(\left(x^{\frac{1}{3}}\right)^{\frac{2}{3}}\\= x^{ \frac{1}{3} . \frac{2}{3} }= x^{\frac{2}{9}}\\=\sqrt[9]{ x^{2} }\\---------------\)
11. \(\left(x^{\frac{1}{2}}\right)^{-1}\\= x^{ \frac{1}{2} . (-1) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
12. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-4}{5}}\\= y^{ \frac{-1}{3} . (\frac{-4}{5}) }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)