Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{2}}\right)^{2}\\= x^{ \frac{-1}{2} . 2 }= x^{-1}\\=\frac{1}{x}\\---------------\)
2. \(\left(a^{\frac{3}{4}}\right)^{\frac{5}{4}}\\= a^{ \frac{3}{4} . \frac{5}{4} }= a^{\frac{15}{16}}\\=\sqrt[16]{ a^{15} }\\---------------\)
3. \(\left(y^{\frac{-1}{4}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-1}{4} . (\frac{-5}{6}) }= y^{\frac{5}{24}}\\=\sqrt[24]{ y^{5} }\\---------------\)
4. \(\left(x^{-1}\right)^{1}\\= x^{ -1 . 1 }= x^{-1}\\=\frac{1}{x}\\---------------\)
5. \(\left(y^{\frac{1}{3}}\right)^{\frac{1}{6}}\\= y^{ \frac{1}{3} . \frac{1}{6} }= y^{\frac{1}{18}}\\=\sqrt[18]{ y }\\---------------\)
6. \(\left(q^{-1}\right)^{\frac{1}{4}}\\= q^{ -1 . \frac{1}{4} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
7. \(\left(q^{\frac{1}{5}}\right)^{\frac{2}{5}}\\= q^{ \frac{1}{5} . \frac{2}{5} }= q^{\frac{2}{25}}\\=\sqrt[25]{ q^{2} }\\---------------\)
8. \(\left(y^{1}\right)^{\frac{-3}{2}}\\= y^{ 1 . (\frac{-3}{2}) }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
9. \(\left(q^{\frac{-1}{3}}\right)^{\frac{4}{3}}\\= q^{ \frac{-1}{3} . \frac{4}{3} }= q^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ q^{4} }}=\frac{1}{\sqrt[9]{ q^{4} }}. \color{purple}{\frac{\sqrt[9]{ q^{5} }}{\sqrt[9]{ q^{5} }}} \\=\frac{\sqrt[9]{ q^{5} }}{q}\\---------------\)
10. \(\left(q^{\frac{1}{6}}\right)^{\frac{1}{5}}\\= q^{ \frac{1}{6} . \frac{1}{5} }= q^{\frac{1}{30}}\\=\sqrt[30]{ q }\\---------------\)
11. \(\left(y^{\frac{-2}{5}}\right)^{\frac{2}{5}}\\= y^{ \frac{-2}{5} . \frac{2}{5} }= y^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ y^{4} }}=\frac{1}{\sqrt[25]{ y^{4} }}. \color{purple}{\frac{\sqrt[25]{ y^{21} }}{\sqrt[25]{ y^{21} }}} \\=\frac{\sqrt[25]{ y^{21} }}{y}\\---------------\)
12. \(\left(a^{\frac{2}{3}}\right)^{\frac{5}{3}}\\= a^{ \frac{2}{3} . \frac{5}{3} }= a^{\frac{10}{9}}\\=\sqrt[9]{ a^{10} }=a.\sqrt[9]{ a }\\---------------\)