Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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