Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-2}{3}}\right)^{\frac{5}{3}}\\= y^{ \frac{-2}{3} . \frac{5}{3} }= y^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ y^{10} }}\\=\frac{1}{y.\sqrt[9]{ y }}=\frac{1}{y.\sqrt[9]{ y }} \color{purple}{\frac{\sqrt[9]{ y^{8} }}{\sqrt[9]{ y^{8} }}} \\=\frac{\sqrt[9]{ y^{8} }}{y^{2}}\\---------------\)
2. \(\left(x^{\frac{-5}{3}}\right)^{1}\\= x^{ \frac{-5}{3} . 1 }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
3. \(\left(q^{\frac{-5}{4}}\right)^{\frac{-5}{2}}\\= q^{ \frac{-5}{4} . (\frac{-5}{2}) }= q^{\frac{25}{8}}\\=\sqrt[8]{ q^{25} }=|q^{3}|.\sqrt[8]{ q }\\---------------\)
4. \(\left(y^{\frac{1}{5}}\right)^{\frac{1}{3}}\\= y^{ \frac{1}{5} . \frac{1}{3} }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
5. \(\left(x^{\frac{-3}{4}}\right)^{\frac{1}{4}}\\= x^{ \frac{-3}{4} . \frac{1}{4} }= x^{\frac{-3}{16}}\\=\frac{1}{\sqrt[16]{ x^{3} }}=\frac{1}{\sqrt[16]{ x^{3} }}. \color{purple}{\frac{\sqrt[16]{ x^{13} }}{\sqrt[16]{ x^{13} }}} \\=\frac{\sqrt[16]{ x^{13} }}{|x|}\\---------------\)
6. \(\left(q^{-1}\right)^{\frac{-1}{5}}\\= q^{ -1 . (\frac{-1}{5}) }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
7. \(\left(q^{\frac{1}{6}}\right)^{\frac{5}{4}}\\= q^{ \frac{1}{6} . \frac{5}{4} }= q^{\frac{5}{24}}\\=\sqrt[24]{ q^{5} }\\---------------\)
8. \(\left(x^{-1}\right)^{\frac{-2}{5}}\\= x^{ -1 . (\frac{-2}{5}) }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
9. \(\left(q^{\frac{-5}{2}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-5}{2} . (\frac{-2}{5}) }= q^{1}\\\\---------------\)
10. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{1}{2} . \frac{1}{2} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
11. \(\left(a^{1}\right)^{\frac{-1}{3}}\\= a^{ 1 . (\frac{-1}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
12. \(\left(y^{\frac{-1}{5}}\right)^{2}\\= y^{ \frac{-1}{5} . 2 }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)