Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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