Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-5}{4}}\right)^{\frac{1}{6}}\\= q^{ \frac{-5}{4} . \frac{1}{6} }= q^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ q^{5} }}=\frac{1}{\sqrt[24]{ q^{5} }}. \color{purple}{\frac{\sqrt[24]{ q^{19} }}{\sqrt[24]{ q^{19} }}} \\=\frac{\sqrt[24]{ q^{19} }}{|q|}\\---------------\)
2. \(\left(x^{\frac{-2}{5}}\right)^{\frac{4}{5}}\\= x^{ \frac{-2}{5} . \frac{4}{5} }= x^{\frac{-8}{25}}\\=\frac{1}{\sqrt[25]{ x^{8} }}=\frac{1}{\sqrt[25]{ x^{8} }}. \color{purple}{\frac{\sqrt[25]{ x^{17} }}{\sqrt[25]{ x^{17} }}} \\=\frac{\sqrt[25]{ x^{17} }}{x}\\---------------\)
3. \(\left(a^{\frac{1}{4}}\right)^{\frac{5}{6}}\\= a^{ \frac{1}{4} . \frac{5}{6} }= a^{\frac{5}{24}}\\=\sqrt[24]{ a^{5} }\\---------------\)
4. \(\left(y^{\frac{-3}{2}}\right)^{\frac{3}{4}}\\= y^{ \frac{-3}{2} . \frac{3}{4} }= y^{\frac{-9}{8}}\\=\frac{1}{\sqrt[8]{ y^{9} }}\\=\frac{1}{|y|.\sqrt[8]{ y }}=\frac{1}{|y|.\sqrt[8]{ y }} \color{purple}{\frac{\sqrt[8]{ y^{7} }}{\sqrt[8]{ y^{7} }}} \\=\frac{\sqrt[8]{ y^{7} }}{|y^{2}|}\\---------------\)
5. \(\left(x^{1}\right)^{2}\\= x^{ 1 . 2 }= x^{2}\\\\---------------\)
6. \(\left(y^{\frac{3}{5}}\right)^{1}\\= y^{ \frac{3}{5} . 1 }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
7. \(\left(a^{\frac{-5}{2}}\right)^{\frac{3}{2}}\\= a^{ \frac{-5}{2} . \frac{3}{2} }= a^{\frac{-15}{4}}\\=\frac{1}{\sqrt[4]{ a^{15} }}\\=\frac{1}{|a^{3}|.\sqrt[4]{ a^{3} }}=\frac{1}{|a^{3}|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{4}|}\\---------------\)
8. \(\left(q^{\frac{-1}{4}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-1}{4} . (\frac{-1}{2}) }= q^{\frac{1}{8}}\\=\sqrt[8]{ q }\\---------------\)
9. \(\left(q^{\frac{1}{5}}\right)^{-1}\\= q^{ \frac{1}{5} . (-1) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
10. \(\left(a^{\frac{-5}{6}}\right)^{-1}\\= a^{ \frac{-5}{6} . (-1) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
11. \(\left(a^{\frac{4}{5}}\right)^{\frac{-5}{3}}\\= a^{ \frac{4}{5} . (\frac{-5}{3}) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
12. \(\left(y^{\frac{3}{4}}\right)^{\frac{-2}{3}}\\= y^{ \frac{3}{4} . (\frac{-2}{3}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)