Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-5}{2}}\right)^{-1}\\= x^{ \frac{-5}{2} . (-1) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
2. \(\left(a^{\frac{4}{3}}\right)^{\frac{-1}{4}}\\= a^{ \frac{4}{3} . (\frac{-1}{4}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
3. \(\left(x^{\frac{-4}{3}}\right)^{1}\\= x^{ \frac{-4}{3} . 1 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
4. \(\left(y^{\frac{-2}{3}}\right)^{1}\\= y^{ \frac{-2}{3} . 1 }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
5. \(\left(y^{\frac{2}{3}}\right)^{\frac{5}{4}}\\= y^{ \frac{2}{3} . \frac{5}{4} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
6. \(\left(a^{1}\right)^{\frac{5}{3}}\\= a^{ 1 . \frac{5}{3} }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
7. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-3}{5}}\\= q^{ \frac{-5}{6} . (\frac{-3}{5}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
8. \(\left(a^{\frac{-1}{5}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-1}{5} . (\frac{-4}{3}) }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
9. \(\left(a^{\frac{1}{5}}\right)^{\frac{-2}{3}}\\= a^{ \frac{1}{5} . (\frac{-2}{3}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
10. \(\left(x^{\frac{4}{3}}\right)^{\frac{1}{3}}\\= x^{ \frac{4}{3} . \frac{1}{3} }= x^{\frac{4}{9}}\\=\sqrt[9]{ x^{4} }\\---------------\)
11. \(\left(x^{\frac{5}{4}}\right)^{\frac{-1}{2}}\\= x^{ \frac{5}{4} . (\frac{-1}{2}) }= x^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ x^{5} }}=\frac{1}{\sqrt[8]{ x^{5} }}. \color{purple}{\frac{\sqrt[8]{ x^{3} }}{\sqrt[8]{ x^{3} }}} \\=\frac{\sqrt[8]{ x^{3} }}{|x|}\\---------------\)
12. \(\left(y^{\frac{-5}{4}}\right)^{\frac{1}{2}}\\= y^{ \frac{-5}{4} . \frac{1}{2} }= y^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ y^{5} }}=\frac{1}{\sqrt[8]{ y^{5} }}. \color{purple}{\frac{\sqrt[8]{ y^{3} }}{\sqrt[8]{ y^{3} }}} \\=\frac{\sqrt[8]{ y^{3} }}{|y|}\\---------------\)