Question

Pqr=a^x , qrs=a^y ,rsp=a^z then pqrs=?

Answer 1

$Given \: pqr = a^x \: ---(1), \\ qrs = a^y \: ---(2)\: and \\ rsp = a^z \: --(3)$

/* Multiplying equations (1), (2) and (3) , we get */

$( pqr ) \times (qrs ) \times (rsp) = a^x \times a^{y} \times a^{z}$

$\implies p^{2} \times r^{2} \times q^{2} \times s^{2} = a^{ x + y + z }$

/* By Exponential Law */

$\boxed { \pink { a^{m} \times a^{n} = a^{m+n} }}$

$\implies (pqrs)^{2} = a^{ x + y + z }$

$\implies pqrs = a^{\frac{ x + y + z}{2} }$

Therefore.,

$\red{ Value \:of \: pqrs} \green { = a^{\frac{ x + y + z}{2} }}$

•••♪