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[tex]125 {}^{ - 3} =( 5 {}^{3} ) {}^{ - 3} = 5 {}^{ - 9} [/tex]

[tex]25 {}^{4} = ({5}^{2} ) {}^{4} = 5 {}^{8} [/tex]

[tex] \frac{5}{25 {}^{4} \times {125}^{ - 3} } = \frac{5}{5 {}^{8} \times {5}^{ - 9} } = \frac{1}{5 {}^{ 7} \times {5}^{ - 9}} = \\ = \frac{1}{ {5}^{ - 2} } = {5}^{ 2} = 25[/tex]

Explicație pas cu pas:

[tex] \dfrac{5}{25^{4} \cdot 125^{ - 3} } =\dfrac{5}{( {5}^{2}) ^{4} \cdot ( {5}^{3})^{ - 3} } =[/tex]

[tex]\dfrac{5}{{5}^{2 \cdot4} \cdot {5}^{3 \cdot(- 3)} }= \dfrac{5}{5^{8} \cdot {5}^{ - 9} } = \dfrac{5}{5^{ 8 + ( - 9)}} = [/tex]

[tex] \dfrac{5}{ {5}^{ - 1} } = 5 : \dfrac{1}{5} = 5 \cdot 5 = \red{ \underline{25}}[/tex]