Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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