Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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