Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{4}{3}}\right)^{-2}\\= y^{ \frac{4}{3} . (-2) }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
2. \(\left(y^{\frac{1}{4}}\right)^{1}\\= y^{ \frac{1}{4} . 1 }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
3. \(\left(q^{\frac{4}{3}}\right)^{\frac{1}{5}}\\= q^{ \frac{4}{3} . \frac{1}{5} }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)
4. \(\left(y^{\frac{-5}{4}}\right)^{1}\\= y^{ \frac{-5}{4} . 1 }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
5. \(\left(y^{\frac{5}{4}}\right)^{-2}\\= y^{ \frac{5}{4} . (-2) }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
6. \(\left(a^{\frac{-2}{5}}\right)^{\frac{1}{3}}\\= a^{ \frac{-2}{5} . \frac{1}{3} }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
7. \(\left(x^{\frac{-1}{5}}\right)^{\frac{5}{4}}\\= x^{ \frac{-1}{5} . \frac{5}{4} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
8. \(\left(a^{\frac{1}{2}}\right)^{\frac{-5}{2}}\\= a^{ \frac{1}{2} . (\frac{-5}{2}) }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
9. \(\left(q^{-2}\right)^{1}\\= q^{ -2 . 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
10. \(\left(y^{\frac{2}{5}}\right)^{\frac{3}{2}}\\= y^{ \frac{2}{5} . \frac{3}{2} }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
11. \(\left(x^{\frac{-4}{3}}\right)^{-1}\\= x^{ \frac{-4}{3} . (-1) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
12. \(\left(q^{\frac{-1}{3}}\right)^{\frac{4}{3}}\\= q^{ \frac{-1}{3} . \frac{4}{3} }= q^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ q^{4} }}=\frac{1}{\sqrt[9]{ q^{4} }}. \color{purple}{\frac{\sqrt[9]{ q^{5} }}{\sqrt[9]{ q^{5} }}} \\=\frac{\sqrt[9]{ q^{5} }}{q}\\---------------\)