Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-3}{4} . (\frac{-1}{3}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
2. \(\left(y^{1}\right)^{\frac{5}{2}}\\= y^{ 1 . \frac{5}{2} }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
3. \(\left(q^{\frac{-5}{2}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-5}{2} . (\frac{-1}{2}) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
4. \(\left(x^{\frac{1}{4}}\right)^{\frac{1}{6}}\\= x^{ \frac{1}{4} . \frac{1}{6} }= x^{\frac{1}{24}}\\=\sqrt[24]{ x }\\---------------\)
5. \(\left(a^{\frac{2}{3}}\right)^{\frac{-4}{3}}\\= a^{ \frac{2}{3} . (\frac{-4}{3}) }= a^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ a^{8} }}=\frac{1}{\sqrt[9]{ a^{8} }}. \color{purple}{\frac{\sqrt[9]{ a }}{\sqrt[9]{ a }}} \\=\frac{\sqrt[9]{ a }}{a}\\---------------\)
6. \(\left(y^{\frac{3}{5}}\right)^{\frac{-3}{5}}\\= y^{ \frac{3}{5} . (\frac{-3}{5}) }= y^{\frac{-9}{25}}\\=\frac{1}{\sqrt[25]{ y^{9} }}=\frac{1}{\sqrt[25]{ y^{9} }}. \color{purple}{\frac{\sqrt[25]{ y^{16} }}{\sqrt[25]{ y^{16} }}} \\=\frac{\sqrt[25]{ y^{16} }}{y}\\---------------\)
7. \(\left(q^{1}\right)^{\frac{5}{4}}\\= q^{ 1 . \frac{5}{4} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
8. \(\left(q^{\frac{4}{5}}\right)^{\frac{-5}{3}}\\= q^{ \frac{4}{5} . (\frac{-5}{3}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
9. \(\left(y^{\frac{-1}{3}}\right)^{\frac{1}{2}}\\= y^{ \frac{-1}{3} . \frac{1}{2} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
10. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-3}{2}}\\= q^{ \frac{-4}{3} . (\frac{-3}{2}) }= q^{2}\\\\---------------\)
11. \(\left(y^{-1}\right)^{\frac{5}{4}}\\= y^{ -1 . \frac{5}{4} }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
12. \(\left(y^{\frac{1}{3}}\right)^{\frac{-1}{5}}\\= y^{ \frac{1}{3} . (\frac{-1}{5}) }= y^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ y }}=\frac{1}{\sqrt[15]{ y }}. \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y}\\---------------\)