Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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