Prove that: 25x2x4 5-2²×10x=6 =125x².
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Answer:
25 × 2x^-4 ÷ 5^-2 × 10x^-6 = 125x^2
25×2×x^2×25=1250x^2
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[tex]\sf{\leadsto \dfrac{25×2x^{-4}}{5^{-2}×10x^{-6}} = 125x² }[/tex]
[tex]\sf{\leadsto \dfrac{5² × \cancel{2} × x^{-4}}{5^{-2} × 5¹ × \cancel{2} × x^{-6}}= 125x²}[/tex]
[tex]\sf{\leadsto \dfrac{5² × x^{-4-(-6) }}{5^{-2+1}} = 125x² }[/tex]
[tex]\sf{\leadsto \dfrac{5² × x^{-4+6}}{5^{-1}} = 125x² }[/tex]
[tex]\sf{\leadsto 5^{2-(-1)} × x² = 125x²}[/tex]
[tex]\sf{\leadsto 5^{2+1}×x² = 125x² }[/tex]
[tex]\sf{\leadsto 5³ × x² = 125x² }[/tex]
[tex]\sf{\leadsto 5 × 5 × 5 × x² = 125x² }[/tex]
[tex]\sf{\leadsto 125x² = 125x² }[/tex]
[tex]\sf{\leadsto L. H. S = R. H. S}[/tex]
[tex]\sf{\leadsto Hence ~Proved ✔ }[/tex]
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[tex]\bold{Thanks~♪:)}[/tex]