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

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

$\left(2^{(2-2)}a^{(-3\cdot 2+5\cdot (-2))}b^{(4\cdot 2+1\cdot (-2))}\right)^-1\\\\=\left(2^{0}a^{-16}b^{6}\right)^{-1}\\\\=\dfrac{a^{16}}{b^{6}}$

None of these answer choices matches the given expression.

Answer 2

C. Correct  for e2020