Question

(______×7)²=441

2⁷×2______=2¹⁵

(7×11)___=7⁷×11⁷​

Answer 1

1.

$(3 + 7 {)}^{2} = 441 \\ {3}^{2} + {7}^{2} = 441 \\ 9 + 49 = 441 \\ 441 = 441 \\ LHS = RHS$

IDENTITY:- (a×b)¹ = a¹ × b¹

2.

${2}^{7} + {2}^{8} = {2}^{15} \\ {2}^{7 + 8} = {2}^{15} \\ {2}^{15} = {2}^{15}$

LHS = RHS

IDENTITY:- a¹ × a² = a¹+²

3. (7×11)⁷ = 7⁷ + 11⁷

7⁷ + 11⁷ = 7⁷ + 11⁷

LHS = RHS

IDENTITY:- (a×b)¹ = a¹ × b¹

[ Here consider 1 as x and 2 as y ]