Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{1}{3}}\right)^{\frac{3}{5}}\\= a^{ \frac{1}{3} . \frac{3}{5} }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
2. \(\left(q^{\frac{5}{3}}\right)^{\frac{1}{5}}\\= q^{ \frac{5}{3} . \frac{1}{5} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
3. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-4}{5} . (\frac{-2}{3}) }= x^{\frac{8}{15}}\\=\sqrt[15]{ x^{8} }\\---------------\)
4. \(\left(y^{\frac{-5}{4}}\right)^{\frac{4}{5}}\\= y^{ \frac{-5}{4} . \frac{4}{5} }= y^{-1}\\=\frac{1}{y}\\---------------\)
5. \(\left(y^{\frac{1}{6}}\right)^{\frac{-1}{4}}\\= y^{ \frac{1}{6} . (\frac{-1}{4}) }= y^{\frac{-1}{24}}\\=\frac{1}{\sqrt[24]{ y }}=\frac{1}{\sqrt[24]{ y }}. \color{purple}{\frac{\sqrt[24]{ y^{23} }}{\sqrt[24]{ y^{23} }}} \\=\frac{\sqrt[24]{ y^{23} }}{|y|}\\---------------\)
6. \(\left(x^{\frac{2}{3}}\right)^{\frac{5}{3}}\\= x^{ \frac{2}{3} . \frac{5}{3} }= x^{\frac{10}{9}}\\=\sqrt[9]{ x^{10} }=x.\sqrt[9]{ x }\\---------------\)
7. \(\left(x^{\frac{-3}{5}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-3}{5} . (\frac{-5}{6}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
8. \(\left(x^{1}\right)^{\frac{-1}{3}}\\= x^{ 1 . (\frac{-1}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
9. \(\left(a^{\frac{5}{3}}\right)^{-1}\\= a^{ \frac{5}{3} . (-1) }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
10. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-3}{5}}\\= a^{ \frac{-3}{4} . (\frac{-3}{5}) }= a^{\frac{9}{20}}\\=\sqrt[20]{ a^{9} }\\---------------\)
11. \(\left(q^{\frac{-1}{5}}\right)^{\frac{1}{6}}\\= q^{ \frac{-1}{5} . \frac{1}{6} }= q^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ q }}=\frac{1}{\sqrt[30]{ q }}. \color{purple}{\frac{\sqrt[30]{ q^{29} }}{\sqrt[30]{ q^{29} }}} \\=\frac{\sqrt[30]{ q^{29} }}{|q|}\\---------------\)
12. \(\left(x^{\frac{-5}{6}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-5}{6} . (\frac{-1}{2}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)