Question

prove this question ​

Answer 1

Topic :-

Exponent and Powers

To Prove :-

$(11)^2 \times (-11)^{-6} = \dfrac{1}{({(11)^2})^2}$

Formula to be Used :-

$a^{-x}=\dfrac{1}{a^x}$

$\dfrac{a^m}{a^n}=a^{m-n}$

$(a^m)^n = a^{mn}$

Solution :-

Solving LHS,

$(11)^2 \times (-11)^{-6}$

$Using, \:a^{-x}=\dfrac{1}{a^x},\: we\:can\:write\:it\:as\: :$

$(11)^2 \times \left (\dfrac{-1}{11} \right)^6$

$(11)^2 \times \dfrac{(-1)^6}{(11)^6}$

$(11)^2 \times \dfrac{1}{(11)^6}$

$as\:\:(-1)^6=1$

$\dfrac{(11)^2}{(11)^6}$

$Using,\:\dfrac{a^m}{a^n}=a^{m-n},\:we\:can\:write\:it\:as\: :$

$(11)^{2-6}$

$(11)^{-4}$

Solving RHS,

$\dfrac{1}{({(11)^2})^2}$

$Using,(a^m)^n = a^{mn}\:we\:can\:write\:it\:as\: :$

$\dfrac{1}{(11)^4}$

$(11)^{-4}$

We can observe that LHS = RHS,

Hence, Proved.

Answer 2

Step-by-step explanation:

$\huge\sf\underline\red{answer}$

given to prove that,

(11)²×(-11)^-6 = [1/(11)²]²

(11)²×(11)^-6 = 1/11⁴

(11)^2-6 = 11^-4

11^-4 = 11^-4