Answer:
1
Step-by-step explanation:
Using the rules of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
Given
[tex](\frac{1}{x^{(a-b)}) } ^{a+b}[/tex] × [tex](\frac{1}{x^{b+a}) } ^{b-a}[/tex]
= [tex]\frac{1}{x^{(a-b)(a+b)} }[/tex] × [tex]\frac{1}{x^{(b+a)(b-a)} }[/tex]
= [tex]\frac{1}{x^{(a^2-b^2)} }[/tex] × [tex]\frac{1}{x^{(b^2-a^2)} }[/tex]
= [tex]\frac{1}{x^{(a^2-b^2+b^2-a^2)} }[/tex]
= [tex]\frac{1}{x^{0} }[/tex]
= [tex]\frac{1}{1}[/tex]
= 1
