Evaluate 5

^{-3log52}x 2^{2log23}-
**A.**

8 -
**B.**

1^{1}/_{8} -
**C.**^{2}/_{5} -
**D.**^{1}/_{8}

##### Correct Answer: Option B

##### Explanation

5^{-3log52} x 2^{2log23}*i* Let -3log_{5}2 = p => log_{5}2^{-3} = p

∴2^{-3} = 5^{p}

∴5^{-3log52} = 5log_{5}2^{-3} = 5^{p}*ii* 2^{2log23} = q => log_{5}3^{2} = q

∴3^{2} = 2^{q}

∴2^{22log23} = 2^{q}

= 3^{2} = 9*i x ii* = 2^{-3} x 9 = ^{1}/_{23} x 9

= ^{1}/_{8} x 9

= ^{9}/_{8} = 1^{1}/_{8}