Question

May someone please help me with the equation? I would be so very thankful.

Answer 1

`\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^(-n) \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^(-n)} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^(-m)\implies a^(n-m) \\\\[-0.35em] ~\dotfill`

`\bf \cfrac{4(3x^2y^4)^3}{(2x^3y^5)^4}\implies \cfrac{4(3^3x^(2\cdot 3)y^(4\cdot 3))}{(2^4x^(3\cdot 4)y^(5\cdot 4))}\implies \cfrac{4(27)x^6y^(12)}{16x^(12)y^(20)}\implies \cfrac{108x^6y^(12)}{16x^(12)y^(20)} \\\\\\ \cfrac{108}{16x^(12)x^(-6)y^(20)y^(-12)}\implies \cfrac{108}{16x^(12-6)y^(20-12)}\implies \cfrac{27}{4x^6 y^8}`