Question

W(5w^3)^-2/w^-4

Can anyone explain this one?

Doing a refresher

Answer 1

`\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^( n)} \qquad \qquad \cfrac{1}{a^( n)}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}} \\\\ -------------------------------\\\\`


`\bf \cfrac{w(5w^3)^(-2)}{w^(-4)}\implies \cfrac{w(5^(-2)w^(-2\cdot 3))}{w^(-4)}\implies \cfrac{w\cdot w^(-6)\cdot 5^(-2)}{w^(-4)}\implies \cfrac{w\cdot w^(-6)\cdot w^(4)}{5^2} \\\\\\ \cfrac{w^(1-6+4)}{5^2}\implies \cfrac{w^(-1)}{5^2}\implies \cfrac{(1)/(w)}{5^2}\implies \cfrac{(1)/(w)}{(5^2)/(1)}\implies \cfrac{1}{w}\cdot \cfrac{1}{5^2}\implies \cfrac{1}{25w}`

usually, when all you have is factors atop and at the bottom, you can simply move then about, just change the sign if from the bottom to the top or from the top to the bottom, and then combine any that may have the same base, like for example


`\bf \cfrac{x^ay^(-b)z^c}{x^(-d)y^ez^f}\implies \cfrac{x^ax^dz^cz^(-f)}{y^ey^b}\implies \cfrac{x^(a+d)z^(c-f)}{y^(e+b)}`