The value of $${\left( {{x^{\frac{{b + c}}{{c - a}}}}} \right)^{\frac{1}{{a - b}}}}{\text{.}}$$ $${\left( {{x^{\frac{{c + a}}{{a - b}}}}} \right)^{\frac{1}{{b - c}}}}.$$ $${\left( {{x^{\frac{{a + b}}{{b - c}}}}} \right)^{\frac{1}{{c - a}}}}{\text{ is = ?}}$$
A. 1
B. a
C. b
D. c
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & {x^{\frac{{b + c}}{{\left( {a - b} \right)\left( {c - a} \right)}}}}.{x^{\frac{{c + a}}{{\left( {a - b} \right)\left( {b - c} \right)}}}}.{x^{\frac{{a + b}}{{\left( {b - c} \right)\left( {c - a} \right)}}}} \cr & = {x^{\frac{{\left( {b + c} \right)\left( {b - c} \right) + \left( {c + a} \right)\left( {c - a} \right) + \left( {a + b} \right)\left( {a - b} \right)}}{{\left( {a - b} \right)\left( {b - c} \right)\left( {c - a} \right)}}}} \cr & = {x^{\frac{{\left( {{b^2} - {c^2}} \right) + \left( {{c^2} - {a^2}} \right) + \left( {{a^2} - {b^2}} \right)}}{{\left( {a - b} \right)\left( {b - c} \right)\left( {c - a} \right)}}}} \cr & = {x^0} \cr & = 1 \cr} $$Related Questions on Surds and Indices
A. $$\frac{1}{2}$$
B. 1
C. 2
D. $$\frac{7}{2}$$
Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:
A. 1.45
B. 1.88
C. 2.9
D. 3.7
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