EXPONENTIALS 3

If (x⁴)(y²) = 2500; find x and y.

solution

(x⁴)(y²) = 2500  [500=2x2x5x5x5 by prime factorization].

(x⁴)(y²) = (5⁴ )x (2²)     [ since 2500=5⁴ x 2²].

equating equal powers,

(x⁴) = (5⁴)     

x   =   5    [equal powers will cancel out]

          also,

(y²) = (2²)

 y    =   2     [equal powers will cancel out]

∴ x   =   5 and y    =   2

TRY THIS…………

If (x³)(y⁵) = 1944; find x and y.