Potęga ilorazu liczb x i y jest równa ilorazowi potęg tych liczb.
- [tex]\huge\boxed{\left(\dfrac{x}{y} \right)^{n}}[/tex] - potęga ilorazu , zał. y≠0
- [tex]\huge\boxed{\dfrac{x^{n} }{y^{n} } }[/tex] - iloraz potęg , zał. y≠0
- [tex]\huge\boxed{\left(\dfrac{x}{y} \right)^{n}= \dfrac{x^{n} }{y^{n} } ,~~zal.~~y\neq 0 }[/tex]
Przedstawiamy potęgę w postaci ilorazu:
[tex]\huge\boxed{a}~~\left(\dfrac{ab}{c} \right)^{6}= \dfrac{a^{6}b^{6} }{c^{6} } ,~~zal.~~c\neq 0 \\\\\huge\boxed{b}~~\left(\dfrac{-2xy}{3z} \right)^{2}= \dfrac{(-2)^{2} x^{2}y^{2} }{3^{2} z^{2} } = \dfrac{4 x^{2}y^{2} }{9z^{2} } ,~~zal.~~z\neq 0[/tex]
[tex]\huge\boxed{c}~~(0,2\div a)^{4} =\left(\dfrac{1}{5} \cdot \dfrac{1}{a} \right)^{4} =\left( \dfrac{1}{5a} \right)^{4}=\dfrac{1^{4} }{5^{2} a^{4} } =\dfrac{1}{625a^{4} } ,~~zal.a\neq 0[/tex]
[tex]\huge\boxed{d}~~\left(\dfrac{1,5c}{d} \right)^{2}=\left(\dfrac{3c}{2d} \right)^{2} =\dfrac{3^{2}c^{2} }{2^{2} d^{2} } = \dfrac{9c^{2} }{4 d^{2} } ,~~zal.~~d\neq 0[/tex]
[tex]\huge\boxed{e}~~\left(\dfrac{-0,1ac}{mn} \right)^{3}=\left(\dfrac{-1ac}{10mn} \right)^{3} =\dfrac{(-1)^{3}a^{3} c^{3} }{10^{3} m^{3} n^{3} } = -\dfrac{a^{3} c^{3} }{1000m^{3} n^{3} } ,~~zal.~~m\neq 0 ,~~n\neq 0[/tex]
[tex]\huge\boxed{f}~~\left(\dfrac{-5x}{3y} \right)^{2} =\dfrac{(-5)^{2}x^{2} }{3^{2} y^{2} } = \dfrac{25x^{2} }{9 y^{2} } ,~~zal.~~y\neq 0[/tex]
