Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-4}{3}}\right)^{\frac{-5}{3}}\\= y^{ \frac{-4}{3} . (\frac{-5}{3}) }= y^{\frac{20}{9}}\\=\sqrt[9]{ y^{20} }=y^{2}.\sqrt[9]{ y^{2} }\\---------------\)
2. \(\left(q^{\frac{-5}{6}}\right)^{1}\\= q^{ \frac{-5}{6} . 1 }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
3. \(\left(x^{\frac{5}{4}}\right)^{\frac{1}{4}}\\= x^{ \frac{5}{4} . \frac{1}{4} }= x^{\frac{5}{16}}\\=\sqrt[16]{ x^{5} }\\---------------\)
4. \(\left(q^{\frac{-2}{5}}\right)^{-1}\\= q^{ \frac{-2}{5} . (-1) }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
5. \(\left(y^{1}\right)^{-1}\\= y^{ 1 . (-1) }= y^{-1}\\=\frac{1}{y}\\---------------\)
6. \(\left(a^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= a^{ \frac{1}{2} . \frac{1}{2} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
7. \(\left(x^{\frac{1}{5}}\right)^{\frac{2}{3}}\\= x^{ \frac{1}{5} . \frac{2}{3} }= x^{\frac{2}{15}}\\=\sqrt[15]{ x^{2} }\\---------------\)
8. \(\left(q^{\frac{1}{2}}\right)^{-2}\\= q^{ \frac{1}{2} . (-2) }= q^{-1}\\=\frac{1}{q}\\---------------\)
9. \(\left(x^{\frac{3}{4}}\right)^{-1}\\= x^{ \frac{3}{4} . (-1) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
10. \(\left(x^{\frac{5}{3}}\right)^{\frac{2}{3}}\\= x^{ \frac{5}{3} . \frac{2}{3} }= x^{\frac{10}{9}}\\=\sqrt[9]{ x^{10} }=x.\sqrt[9]{ x }\\---------------\)
11. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-2}{5} . (\frac{-1}{2}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
12. \(\left(q^{\frac{2}{5}}\right)^{\frac{3}{4}}\\= q^{ \frac{2}{5} . \frac{3}{4} }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)