Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-5}{2}}\\= a^{ \frac{-2}{3} . (\frac{-5}{2}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
2. \(\left(a^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{2}{3} . (\frac{-1}{2}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
3. \(\left(a^{\frac{-1}{5}}\right)^{-1}\\= a^{ \frac{-1}{5} . (-1) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
4. \(\left(y^{-1}\right)^{\frac{-1}{2}}\\= y^{ -1 . (\frac{-1}{2}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
5. \(\left(y^{\frac{-4}{5}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-4}{5} . (\frac{-2}{3}) }= y^{\frac{8}{15}}\\=\sqrt[15]{ y^{8} }\\---------------\)
6. \(\left(x^{\frac{4}{5}}\right)^{-1}\\= x^{ \frac{4}{5} . (-1) }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
7. \(\left(q^{\frac{2}{3}}\right)^{\frac{-5}{2}}\\= q^{ \frac{2}{3} . (\frac{-5}{2}) }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
8. \(\left(y^{\frac{-3}{4}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-3}{4} . (\frac{-1}{3}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
9. \(\left(y^{\frac{2}{3}}\right)^{\frac{-1}{5}}\\= y^{ \frac{2}{3} . (\frac{-1}{5}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
10. \(\left(a^{\frac{5}{4}}\right)^{\frac{3}{5}}\\= a^{ \frac{5}{4} . \frac{3}{5} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
11. \(\left(x^{\frac{1}{6}}\right)^{\frac{1}{6}}\\= x^{ \frac{1}{6} . \frac{1}{6} }= x^{\frac{1}{36}}\\=\sqrt[36]{ x }\\---------------\)
12. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{2} . (\frac{-1}{2}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)