Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{2}}\right)^{\frac{4}{5}}\\= x^{ \frac{1}{2} . \frac{4}{5} }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
2. \(\left(a^{\frac{1}{2}}\right)^{\frac{-5}{3}}\\= a^{ \frac{1}{2} . (\frac{-5}{3}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
3. \(\left(x^{\frac{5}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{5}{3} . \frac{1}{2} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
4. \(\left(a^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= a^{ \frac{1}{2} . \frac{1}{2} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
5. \(\left(x^{\frac{1}{3}}\right)^{\frac{5}{4}}\\= x^{ \frac{1}{3} . \frac{5}{4} }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
6. \(\left(x^{\frac{3}{5}}\right)^{-2}\\= x^{ \frac{3}{5} . (-2) }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
7. \(\left(y^{\frac{2}{3}}\right)^{\frac{3}{4}}\\= y^{ \frac{2}{3} . \frac{3}{4} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
8. \(\left(q^{\frac{4}{3}}\right)^{-1}\\= q^{ \frac{4}{3} . (-1) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
9. \(\left(q^{\frac{3}{4}}\right)^{\frac{1}{3}}\\= q^{ \frac{3}{4} . \frac{1}{3} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
10. \(\left(q^{\frac{-2}{5}}\right)^{\frac{2}{5}}\\= q^{ \frac{-2}{5} . \frac{2}{5} }= q^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ q^{4} }}=\frac{1}{\sqrt[25]{ q^{4} }}. \color{purple}{\frac{\sqrt[25]{ q^{21} }}{\sqrt[25]{ q^{21} }}} \\=\frac{\sqrt[25]{ q^{21} }}{q}\\---------------\)
11. \(\left(q^{\frac{-5}{2}}\right)^{\frac{1}{4}}\\= q^{ \frac{-5}{2} . \frac{1}{4} }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
12. \(\left(q^{\frac{5}{3}}\right)^{-1}\\= q^{ \frac{5}{3} . (-1) }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)