Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{3}}\right)^{\frac{1}{3}}\\= x^{ \frac{1}{3} . \frac{1}{3} }= x^{\frac{1}{9}}\\=\sqrt[9]{ x }\\---------------\)
2. \(\left(a^{\frac{-5}{3}}\right)^{1}\\= a^{ \frac{-5}{3} . 1 }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
3. \(\left(y^{2}\right)^{\frac{4}{3}}\\= y^{ 2 . \frac{4}{3} }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
4. \(\left(q^{\frac{-5}{2}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-5}{2} . (\frac{-2}{3}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
5. \(\left(a^{\frac{-3}{2}}\right)^{\frac{-5}{3}}\\= a^{ \frac{-3}{2} . (\frac{-5}{3}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
6. \(\left(y^{\frac{-5}{2}}\right)^{\frac{-4}{5}}\\= y^{ \frac{-5}{2} . (\frac{-4}{5}) }= y^{2}\\\\---------------\)
7. \(\left(a^{\frac{5}{3}}\right)^{-2}\\= a^{ \frac{5}{3} . (-2) }= a^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ a^{10} }}\\=\frac{1}{a^{3}.\sqrt[3]{ a }}=\frac{1}{a^{3}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{4}}\\---------------\)
8. \(\left(x^{\frac{-1}{4}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-1}{4} . (\frac{-1}{2}) }= x^{\frac{1}{8}}\\=\sqrt[8]{ x }\\---------------\)
9. \(\left(a^{\frac{1}{2}}\right)^{-1}\\= a^{ \frac{1}{2} . (-1) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
10. \(\left(q^{\frac{1}{5}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{5} . (\frac{-1}{3}) }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
11. \(\left(y^{-2}\right)^{\frac{-5}{3}}\\= y^{ -2 . (\frac{-5}{3}) }= y^{\frac{10}{3}}\\=\sqrt[3]{ y^{10} }=y^{3}.\sqrt[3]{ y }\\---------------\)
12. \(\left(a^{\frac{-3}{4}}\right)^{\frac{2}{5}}\\= a^{ \frac{-3}{4} . \frac{2}{5} }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)