Question

Simplify $\frac{8^{3a}\times 2^5\times 2^{2a}}{4\times 2^{11a}\times 2^{-2a}}$

• A. $4\times 2^{2a}$
• B. $2\times 2^{2a}$
  
• C. $8\times 2^{2a}$
  
• D. $16\times 2^{2a}$
  

Answer 1

Answer: (C)

$8\times 2^{2a}$

We have,

$\frac{8^{3a}\times 2^5\times 2^{2a}}{4\times 2^{11a}\times 2^{-2a}}$

$\Rightarrow \frac{(2^3{)}^{3a}\times 2^5\times 2^{2a}}{2^2\times 2^{11a-2a}}$

$\Rightarrow \frac{2^{9a}\times 2^{5+2a}}{2^2\times 2^{9a}}$

$\Rightarrow \frac{2^{5+2a+9a}}{2^{9a+2}}$

$\Rightarrow \frac{2^{5+11a}}{2^{9a+2}}$

$\Rightarrow 2^{5+11a-9a-2}$

$\Rightarrow 2^{2a+3}$

$\Rightarrow 2^{2a}\times 2^3$

$\Rightarrow 8\times 2^{2a}$

Hence, this is the answer.