Question

If a,b,c are positive real numbers, then √a^-1 b ×√b^-1 c ×√c^-1 d is equal ?

(a) 1
(b)abc​

Answer 1

question..

=√b/a×√c/b×√a/c

=√(b/a×c/b×a/c)

=√1

=1

this is your answer

please mark as brain list

Answer 2

Answer:

$\sqrt{a^{-1 }b} \times \sqrt{b^{-1 }c} \times \sqrt{b^{-1 }a}=1$

Step-by-step explanation:

Given a, b, c are positive real numbers.

and then $\sqrt{a^{-1 }b} \times \sqrt{b^{-1 }c} \times \sqrt{b^{-1 }a}$

Using the law of indices, $\sqrt{a}=a^\frac{1}{2}$

$\big(a^{-1 }b\big)^{\dfrac{1}{2}} \times \big(b^{-1 }c\big)^{\dfrac{1}{2}} \times \big(c^{-1 }a\big)^{\dfrac{1}{2}}$

Using the law of indices, $a^{m^n}=a^{mn}$

$a^{^{-\dfrac{1}{2}} }b^{^\dfrac{1}{2}}} \times b^{^{-\dfrac{1}{2}} }c^{^\dfrac{1}{2}}} \times c^{^{-\dfrac{1}{2}} }a^{^\dfrac{1}{2}}}$

Grouping the like terms,

$a^{^{-\dfrac{1}{2}} }a^{^\dfrac{1}{2}}}\times b^{^\dfrac{1}{2}}} b^{^{-\dfrac{1}{2}} }\times c^{^\dfrac{1}{2}}} c^{^{-\dfrac{1}{2}} }$

Using the law of indices, $a^{m}\times a^{n}=a^{mn}$

$a^{^{-\dfrac{1}{2} +\dfrac{1}{2}}}\times b^{^{-\dfrac{1}{2} +\dfrac{1}{2}}}\times c^{^{-\dfrac{1}{2} +\dfrac{1}{2}}}=a^{0}\times b^{0}\times c^{0}$

Using the law of indices, $a^{0}=1$

$1\times 1\times 1=1$

Therefore, $\sqrt{a^{-1 }b} \times \sqrt{b^{-1 }c} \times \sqrt{b^{-1 }a}=1$.

Hence, the correct answer is option a.