Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-5}{2}}\right)^{\frac{4}{3}}\\= x^{ \frac{-5}{2} . \frac{4}{3} }= x^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ x^{10} }}\\=\frac{1}{x^{3}.\sqrt[3]{ x }}=\frac{1}{x^{3}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{4}}\\---------------\)
2. \(\left(q^{\frac{-1}{5}}\right)^{-1}\\= q^{ \frac{-1}{5} . (-1) }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
3. \(\left(y^{\frac{-3}{5}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-3}{5} . (\frac{-1}{3}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
4. \(\left(x^{2}\right)^{\frac{5}{3}}\\= x^{ 2 . \frac{5}{3} }= x^{\frac{10}{3}}\\=\sqrt[3]{ x^{10} }=x^{3}.\sqrt[3]{ x }\\---------------\)
5. \(\left(x^{\frac{1}{2}}\right)^{\frac{-2}{3}}\\= x^{ \frac{1}{2} . (\frac{-2}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
6. \(\left(q^{\frac{-4}{5}}\right)^{-1}\\= q^{ \frac{-4}{5} . (-1) }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
7. \(\left(x^{\frac{1}{4}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{4} . \frac{1}{2} }= x^{\frac{1}{8}}\\=\sqrt[8]{ x }\\---------------\)
8. \(\left(x^{\frac{-3}{5}}\right)^{\frac{-4}{5}}\\= x^{ \frac{-3}{5} . (\frac{-4}{5}) }= x^{\frac{12}{25}}\\=\sqrt[25]{ x^{12} }\\---------------\)
9. \(\left(a^{\frac{1}{2}}\right)^{\frac{-5}{3}}\\= a^{ \frac{1}{2} . (\frac{-5}{3}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
10. \(\left(q^{\frac{-3}{5}}\right)^{\frac{1}{3}}\\= q^{ \frac{-3}{5} . \frac{1}{3} }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
11. \(\left(x^{\frac{1}{6}}\right)^{\frac{-4}{3}}\\= x^{ \frac{1}{6} . (\frac{-4}{3}) }= x^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ x^{2} }}=\frac{1}{\sqrt[9]{ x^{2} }}. \color{purple}{\frac{\sqrt[9]{ x^{7} }}{\sqrt[9]{ x^{7} }}} \\=\frac{\sqrt[9]{ x^{7} }}{x}\\---------------\)
12. \(\left(y^{\frac{-1}{5}}\right)^{\frac{1}{6}}\\= y^{ \frac{-1}{5} . \frac{1}{6} }= y^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ y }}=\frac{1}{\sqrt[30]{ y }}. \color{purple}{\frac{\sqrt[30]{ y^{29} }}{\sqrt[30]{ y^{29} }}} \\=\frac{\sqrt[30]{ y^{29} }}{|y|}\\---------------\)