Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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