Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{3}{4}}\right)^{\frac{-4}{3}}\\= q^{ \frac{3}{4} . (\frac{-4}{3}) }= q^{-1}\\=\frac{1}{q}\\---------------\)
2. \(\left(y^{\frac{-5}{6}}\right)^{\frac{3}{5}}\\= y^{ \frac{-5}{6} . \frac{3}{5} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
3. \(\left(a^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{3} . (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
4. \(\left(x^{\frac{-4}{3}}\right)^{\frac{3}{4}}\\= x^{ \frac{-4}{3} . \frac{3}{4} }= x^{-1}\\=\frac{1}{x}\\---------------\)
5. \(\left(x^{2}\right)^{\frac{-3}{5}}\\= x^{ 2 . (\frac{-3}{5}) }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
6. \(\left(a^{\frac{-1}{4}}\right)^{\frac{-5}{4}}\\= a^{ \frac{-1}{4} . (\frac{-5}{4}) }= a^{\frac{5}{16}}\\=\sqrt[16]{ a^{5} }\\---------------\)
7. \(\left(x^{\frac{1}{6}}\right)^{1}\\= x^{ \frac{1}{6} . 1 }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
8. \(\left(q^{\frac{-2}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{-2}{3} . \frac{1}{2} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
9. \(\left(x^{\frac{-3}{4}}\right)^{-1}\\= x^{ \frac{-3}{4} . (-1) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
10. \(\left(x^{\frac{-3}{4}}\right)^{\frac{5}{4}}\\= x^{ \frac{-3}{4} . \frac{5}{4} }= x^{\frac{-15}{16}}\\=\frac{1}{\sqrt[16]{ x^{15} }}=\frac{1}{\sqrt[16]{ x^{15} }}. \color{purple}{\frac{\sqrt[16]{ x }}{\sqrt[16]{ x }}} \\=\frac{\sqrt[16]{ x }}{|x|}\\---------------\)
11. \(\left(a^{\frac{1}{6}}\right)^{\frac{1}{2}}\\= a^{ \frac{1}{6} . \frac{1}{2} }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
12. \(\left(y^{\frac{2}{5}}\right)^{\frac{-2}{3}}\\= y^{ \frac{2}{5} . (\frac{-2}{3}) }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)