Question

If $\frac{2^{(2a+1)}\times 3^{(3b+2)}}{6^2}=2^x\times 3^y$

Chose the correct option:

• A. x = 2a – 1, y = 3b
• B. x = 2a + 1, y = 3b + 2
• C. x = 2a + 1, y = 3b
• D. x = 2a + 1, y = 3b

Answer 1

The correct option is A

x = 2a – 1, y = 3b

$\frac{2^{(2a+1)}\times 3^{(3b+2)}}{6^2}=\frac{2^{(2a+1)}\times 3^{(3b+2)}}{(2\times 3{)}^2}$

$=\frac{2^{(2a+1)}\times 3^{(3b+2)}}{2^2\times 3^2}$ $[\because (ab{)}^m=a^m\times b^m]$

$=2^{(2a+1-2)}\times 3^{(3b+2-2)}[\because \frac{a^m}{a^n}=a^{m-n}]$

$=2^{(2a-1)}\times 3^{\left(3b\right)}\because 2^{(2a-1)}\times 3^{\left(3b\right)}=2^x\times 3^y$

$\Rightarrow x=2a-1,y=3b$