Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-5}{2}}\\= a^{ \frac{-2}{5} . (\frac{-5}{2}) }= a^{1}\\\\---------------\)
2. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-2}{5} . (\frac{-1}{2}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
3. \(\left(x^{\frac{-4}{5}}\right)^{\frac{2}{3}}\\= x^{ \frac{-4}{5} . \frac{2}{3} }= x^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ x^{8} }}=\frac{1}{\sqrt[15]{ x^{8} }}. \color{purple}{\frac{\sqrt[15]{ x^{7} }}{\sqrt[15]{ x^{7} }}} \\=\frac{\sqrt[15]{ x^{7} }}{x}\\---------------\)
4. \(\left(a^{\frac{-2}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{-2}{3} . \frac{1}{2} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
5. \(\left(y^{\frac{3}{4}}\right)^{\frac{2}{3}}\\= y^{ \frac{3}{4} . \frac{2}{3} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
6. \(\left(a^{1}\right)^{\frac{1}{5}}\\= a^{ 1 . \frac{1}{5} }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
7. \(\left(y^{\frac{3}{4}}\right)^{\frac{1}{5}}\\= y^{ \frac{3}{4} . \frac{1}{5} }= y^{\frac{3}{20}}\\=\sqrt[20]{ y^{3} }\\---------------\)
8. \(\left(a^{\frac{1}{5}}\right)^{\frac{1}{3}}\\= a^{ \frac{1}{5} . \frac{1}{3} }= a^{\frac{1}{15}}\\=\sqrt[15]{ a }\\---------------\)
9. \(\left(q^{\frac{-4}{3}}\right)^{\frac{5}{2}}\\= q^{ \frac{-4}{3} . \frac{5}{2} }= q^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ q^{10} }}\\=\frac{1}{q^{3}.\sqrt[3]{ q }}=\frac{1}{q^{3}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{4}}\\---------------\)
10. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{3}}\\= y^{ \frac{-1}{2} . \frac{1}{3} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
11. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{4}}\\= q^{ \frac{1}{2} . \frac{1}{4} }= q^{\frac{1}{8}}\\=\sqrt[8]{ q }\\---------------\)
12. \(\left(q^{\frac{-2}{5}}\right)^{\frac{2}{5}}\\= q^{ \frac{-2}{5} . \frac{2}{5} }= q^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ q^{4} }}=\frac{1}{\sqrt[25]{ q^{4} }}. \color{purple}{\frac{\sqrt[25]{ q^{21} }}{\sqrt[25]{ q^{21} }}} \\=\frac{\sqrt[25]{ q^{21} }}{q}\\---------------\)