Question

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

A.) 2/3a^4b^10
B.) 4/9a^4b^10
C.) 1/36a^4b^10
D.) 36a^4b^10/1

Answer 1

C. Correct for e2020

Answer 2

Using the rules of exponents

`\left(a^(b)\right)^(c)=a^((b\cdot c))\\a^(b)\cdot a^(c)=a^((b+c))`

you can simplify this to

`\left(2^((2-2))a^((-3\cdot 2+5\cdot (-2)))b^((4\cdot 2+1\cdot (-2)))\right)^-1\\\\=\left(2^(0)a^(-16)b^(6)\right)^(-1)\\\\=(a^(16))/(b^(6))`

None of these answer choices matches the given expression.