Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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