If \(πππ β 0\) and \(π^{βπ₯} = \frac {1} {π} , π ^{βπ¦} = \frac {1} {π}β¦
2018
IfΒ \(πππ β 0\) and \(π^{βπ₯} = \frac {1} {π} , π ^{βπ¦} = \frac {1} {π} , π^{βπ§} = \frac {1} {π }\), what is the value of the product \(π₯π¦π§\)Β ?
- A.
\(β1\) - B.
\(\frac {1} {pqr}\) - C.
\(1\) - D.
\(πππ\)
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Correct answer: C
Given p^{-x} = 1/q, q^{-y} = 1/r, r^{-z} = 1/p and pqr β 0.
Invert each equation to remove negative exponents: p^x = q, q^y = r, r^z = p.
Substitute stepwise: from p^x = q and q^y = r we get p^{xy} = r. Using r^z = p then gives p^{xyz} = p.
Since p β 0, equate exponents to conclude xyz = 1.
Therefore the value of the product xyz is 1.