EXPONENTIALS B3

 

If (x⁵)(y²) = 7500; find x and y.

 

solution

 

(x⁵)(y²) = 7500  [7500=2x2x5x5x5x5x5 by prime factorization].

 

(x⁵)(y²) = (5⁵ )x (2²)     [ since 7500=5⁵ x 2²].

 

equating equal powers,

 

(x⁵) = (5⁵)     

 

x   =   5    [since equal powers cancel out]

 

also,

 

(y²) = (2²) [since equal powers cancel out]

 

 y    =   2

 

∴ x   =   5 and y    =   2

 

TRY THIS…………

 

If (x⁵)(y³) = 15,000; find x and y.