Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{5}{2}}\right)^{\frac{-5}{3}}\\= y^{ \frac{5}{2} . (\frac{-5}{3}) }= y^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ y^{25} }}\\=\frac{1}{|y^{4}|.\sqrt[6]{ y }}=\frac{1}{|y^{4}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{5}|}\\---------------\)
2. \(\left(x^{\frac{4}{5}}\right)^{\frac{-5}{3}}\\= x^{ \frac{4}{5} . (\frac{-5}{3}) }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
3. \(\left(q^{\frac{5}{2}}\right)^{\frac{2}{5}}\\= q^{ \frac{5}{2} . \frac{2}{5} }= q^{1}\\\\---------------\)
4. \(\left(y^{\frac{5}{6}}\right)^{\frac{-1}{4}}\\= y^{ \frac{5}{6} . (\frac{-1}{4}) }= y^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ y^{5} }}=\frac{1}{\sqrt[24]{ y^{5} }}. \color{purple}{\frac{\sqrt[24]{ y^{19} }}{\sqrt[24]{ y^{19} }}} \\=\frac{\sqrt[24]{ y^{19} }}{|y|}\\---------------\)
5. \(\left(x^{-1}\right)^{-1}\\= x^{ -1 . (-1) }= x^{1}\\\\---------------\)
6. \(\left(y^{1}\right)^{\frac{-2}{3}}\\= y^{ 1 . (\frac{-2}{3}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
7. \(\left(q^{1}\right)^{\frac{3}{5}}\\= q^{ 1 . \frac{3}{5} }= q^{\frac{3}{5}}\\=\sqrt[5]{ q^{3} }\\---------------\)
8. \(\left(q^{\frac{2}{3}}\right)^{1}\\= q^{ \frac{2}{3} . 1 }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
9. \(\left(q^{\frac{-2}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{-2}{3} . \frac{1}{2} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
10. \(\left(x^{\frac{5}{4}}\right)^{1}\\= x^{ \frac{5}{4} . 1 }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
11. \(\left(a^{\frac{4}{5}}\right)^{\frac{-4}{5}}\\= a^{ \frac{4}{5} . (\frac{-4}{5}) }= a^{\frac{-16}{25}}\\=\frac{1}{\sqrt[25]{ a^{16} }}=\frac{1}{\sqrt[25]{ a^{16} }}. \color{purple}{\frac{\sqrt[25]{ a^{9} }}{\sqrt[25]{ a^{9} }}} \\=\frac{\sqrt[25]{ a^{9} }}{a}\\---------------\)
12. \(\left(y^{\frac{1}{6}}\right)^{\frac{5}{4}}\\= y^{ \frac{1}{6} . \frac{5}{4} }= y^{\frac{5}{24}}\\=\sqrt[24]{ y^{5} }\\---------------\)