Question

Show that:- xa(b-c)/xb(a-c)divided by (xb/xa)c = 1

Answer 1

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Answer 2

Answer:

The expression xa(b-c)/xb(a-c)divided by (xb/xa)c = 1 is true.

Step-by-step explanation:

We are given:

x(a(b-c))/(x(b(a-c))) ÷ (x(b)/x(a))^c = ?

Let's simplify the expression step by step:

x(a(b-c))/(x(b(a-c))) ÷ (x(b)/x(a))^c

= x(a(b-c))/(x(b(a-c))) * (x(a)/x(b))^c (using the property of division as multiplication with the reciprocal)

= x(a(b-c)) * x(a)^c / (x(b(a-c)) * x(b)^c) (using the property of exponents: (a/b)^c = a^c / b^c)

= x(a^(b-c+c)) / x(b^(a-c+c)) (using the property of exponents: a^b * a^c = a^(b+c))

= x(a^b) / x(b^a)

= 1 / (x(b^a) / x(a^b)) (using the property of reciprocals)

= 1 / ((x(b)/x(a))^a) (using the property of exponents: (a/b)^c = a^c / b^c)

= 1 / ((xb/xa)^a)

= 1

Therefore, we have shown that:

x(a(b-c))/(x(b(a-c))) ÷ (x(b)/x(a))^c = 1

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