Question

plsss answer this question ​

Answer 1

Question :- Evaluate

$\bf \: {x}^{(a + b)(a- b)} \times {x}^{(b + c)(b - c)} \times {x}^{(c + a)(c - a)}$

Answer

Formula used :-

$\bf \: {x}^{m} \times {x}^{n} = {x}^{m + n}$

$\bf \: {x}^{2} - {y}^{2} = (x + y)(x - y)$

$\bf \: {x}^{0} = 1$

Solution :-

$\bf \: {x}^{(a + b)(a- b)} \times {x}^{(b + c)(b - c)} \times {x}^{(c + a)(c - a)}$

$\bf\implies \:\: {x}^{ {a}^{2} - {b}^{2} } \times {x}^{ {b}^{2} - {c}^{2} } \times {x}^{ {c}^{2} - {a}^{2} }$

$\bf\implies \: {x}^{ {a}^{2} - {b}^{2} + {b}^{2} - {c}^{2} + {c}^{2} - {a}^{2} }$

$\bf\implies \: {x}^{0} = 1$