Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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