(x^b/x^c)^{1/{bc}}\times(x^c/x^a)^{1/{ac}}\times(x^a/x^b)^{1/{ab}} is equivalent to:

Surds and Indices Practice Test 2

Question : 3 of 17

Marks: +1, -0

(x^b/x^c)^{1/{bc}}×(x^c/x^a)^{1/{ac}}×(x^a/x^b)^{1/{ab}}

is equivalent to:

Solution:

(x^b/x^c)^{1/{bc}}=(x^{b-c})^{1/{bc}}=x^{(1/c-1/b)}

Similarly,

(x^c/x^a)^{1/{ac}}=x^{(1/a-1/c)}

and

(x^a/x^b)^{1/{ab}}=x^{(1/b-1/a)}

∴(x^b/x^c)^{1/{bc}}×(x^c/x^a)^{1/{ac}}×(x^a/x^b)^{1/{ab}}

=x^{(1/c-1/b)}×x^{(1/a-1/c)}×x^{(1/b-1/a)}

=x^{(1/c-1/b+1/a-1/c+1/b-1/a)}=x^0=1

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