Question

Which number is equivalent to 2^−5⋅ 3 ⋅ 2^2 ⋅ 3^3? A. 648 B. 216 C. 81/8 D. 27/8

Answer 1

$2^{-5} \cdot 3 \cdot 2^2 \cdot 3^3\\\\=2^{-5 +2} \cdot 3^{1+3}\\\\=2^{-3} \cdot 3^4\\\\=\dfrac{3^4}{2^3}\\\\=\dfrac{81}{8}\\\\\\\text{So, the answer is C.}$