Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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