Question

Find $a$, if

$\left(\frac{1}{9}\right)^{-4} \times\left(\frac{1}{27}\right)^{-6}=\left(\frac{1}{9}\right)^{a}$

(A) $13$

(B) $-13$

(C) $15$

(D) $-15$

Answer 1

 $\left(\frac{1}{9}\right)^{a}=\left(\frac{1}{9}\right)^{-4} \times\left(\frac{1}{27}\right)^{-6}$

$\Rightarrow\left(\frac{1}{3}\right)^{2 a}=\left(\frac{1}{3}\right)^{-8} \times\left(\frac{1}{3}\right)^{-18}$

$\Rightarrow\left(\frac{1}{3}\right)^{2 a}=\left(\frac{1}{3}\right)^{-26}$

$\Rightarrow 2 a=-26$

$\therefore \quad a=-\frac{26}{2}=-13 ;$ Ans.

Therefore, The correct option is $(\mathrm{B})$