Question

PLEASE HELP ME! THIS IS SO HARD.

Which expression is equivalent to
`( ((2a^-^3b^4)^2)/((3a^5b)^-^2))^-^1`

Answer 1

`\bf \left[ \cfrac{(2a^(-3)b^4)^2}{(3a^5b)^(-2)} \right]^(-1)\implies \left[ \cfrac{(3a^5b)^(-2)} {(2a^(-3)b^4)^2}\right]\implies \cfrac{(1)/((3a^5b)^(2))} {(2a^(-3)b^4)^2} \\\\\\`


`\bf \cfrac{(1)/((3a^5b)^(2))} {2^2a^(-6)b^8}\implies \cfrac{(1)/((3a^5b)^(2))} {2^2(1)/(a^6)b^8}\implies \cfrac{(1)/(3^2a^(10)b^2)}{(4b^8)/(a^6)}\implies \cfrac{1}{3^2a^(10)b^2}\cdot \cfrac{a^6}{4b^8} \\\\\\ \cfrac{1}{3^24a^(10)b^2b^8}\cdot \cfrac{1}{a^(-6)}\implies \cfrac{1}{9\cdot 4a^(10)a^(-6)b^2b^8} \\\\\\ \cfrac{1}{36a^(10-6)b^(2+8)}\implies \boxed{\cfrac{1}{36a^4b^(10)}}`