Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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