Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{2}}\right)^{1}\\= y^{ \frac{-1}{2} . 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
2. \(\left(x^{1}\right)^{\frac{1}{6}}\\= x^{ 1 . \frac{1}{6} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
3. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-5}{4}}\\= a^{ \frac{-3}{4} . (\frac{-5}{4}) }= a^{\frac{15}{16}}\\=\sqrt[16]{ a^{15} }\\---------------\)
4. \(\left(q^{\frac{-1}{5}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-1}{5} . (\frac{-1}{6}) }= q^{\frac{1}{30}}\\=\sqrt[30]{ q }\\---------------\)
5. \(\left(y^{\frac{-5}{6}}\right)^{1}\\= y^{ \frac{-5}{6} . 1 }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
6. \(\left(q^{2}\right)^{\frac{3}{5}}\\= q^{ 2 . \frac{3}{5} }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)
7. \(\left(a^{\frac{2}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{2}{5} . (\frac{-1}{2}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
8. \(\left(q^{\frac{-1}{5}}\right)^{1}\\= q^{ \frac{-1}{5} . 1 }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
9. \(\left(q^{\frac{-4}{5}}\right)^{\frac{-4}{5}}\\= q^{ \frac{-4}{5} . (\frac{-4}{5}) }= q^{\frac{16}{25}}\\=\sqrt[25]{ q^{16} }\\---------------\)
10. \(\left(x^{\frac{1}{6}}\right)^{\frac{-4}{3}}\\= x^{ \frac{1}{6} . (\frac{-4}{3}) }= x^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ x^{2} }}=\frac{1}{\sqrt[9]{ x^{2} }}. \color{purple}{\frac{\sqrt[9]{ x^{7} }}{\sqrt[9]{ x^{7} }}} \\=\frac{\sqrt[9]{ x^{7} }}{x}\\---------------\)
11. \(\left(y^{\frac{-1}{2}}\right)^{-1}\\= y^{ \frac{-1}{2} . (-1) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
12. \(\left(y^{\frac{-2}{5}}\right)^{2}\\= y^{ \frac{-2}{5} . 2 }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)