Question

Which is the simplified form of the expression (2^-2) (3^4)^-3 x (2^-3) (3^2) ^2?

A: 1/ 2^36 3^48

B: 1/ 3^8

C: 3^8

D:2^36 3^48

Answer 1

The answer is D

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Answer 2

`(2^(-2))(3^4)^(-3)*(2^(-3))(3^2)^2=(2^(-2))(2^(-3))*(3^4)^(-3)(3^2)^2\\\\=2^(-2+(-3))*(3^(4\cdot(-3)))(3^(2\cdot2))=2^(-5)*(3^(-12))(3^4)\\\\=2^(-5)*3^(-12+4)=2^(-5)*3^(-8) =(1)/(2^5\cdot3^8)\\\\\text{used:}\\\\a\cdot b=b\cdot a\\\\a^n\cdot a^m=a^(n+m)\\\\(a^n)^m=a^(n\cdot m)`