Question

Which answer is equivalent to
??? Help please

Answer 1

`\large\boxed{(36)/(25)}`

Explanation:

`\text{Use}\ a^(-n)=(1)/(a^n)\\\\(5^(-2)\cdot9)/(2^4\cdot4^(-3))=(5^(-2)\cdot9):(2^4\cdot4^(-3))=\left((1)/(5^2)\cdot9\right):\left(2^4\cdot(2^2)^(-3)\right)\\\\\text{use}\ (a^n)^m=a^(nm)\\\\=\left((1)/(25)\cdot9\right):(2^4\cdot2^(-6))\\\\\text{use}\ a^n\cdot a^m=a^(n+m)\\\\=(9)/(25):2^(4+(-6))=(9)/(25):2^(-2)=(9)/(25):(1)/(2^2)=(9)/(25):(1)/(4)=(9)/(25)\cdot(4)/(1)=(36)/(25)`