Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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