What is the rate of interest when the P.W. of $ 1245 due in 15 months is $ 1200?

? = ?(13)⁴ = ?13 x 13 x 13 x 13
Apply the rule of square root.
= 13 x 13 = 169

16^3/2 + 16^-3/2
Apply the law of Fractional Exponents and Laws of Exponents
a^m x aⁿ = a^m+n
a^-m = 1/a^m
?16^3/2 + 1/16^3/2
?(16^1/2)³ + 1/(16^1/2)³
?(4^{2 x 1/2})³ + 1/(4^{2 x 1/2})³
?4³ + 1/4³
? 64 + 1/64
? (64 x 64+ 1)/64
= (4096+1)/64
= 4097/64

? = [(12)^-2]²/[(12)²]^-2
Apply the Algebra Law,
(a^m)ⁿ = a^mn
= (12) ^{- 4}/(12) ^{- 4}
= 1

Given that ,(16)⁹ ÷ (16)⁴ x (16) ³ = (16)^?
Apply the law of Fractional Exponents and Laws of Exponents
(a^m) x (aⁿ) = a^{m + n}-------------------1
a^m ÷ aⁿ = a^{m ? n}----------------2
? (16)⁹ ÷ (16)⁴ x (16) ³ = (16)^?
? (16)^? = (16)^{9 + 3 - 4}
? ? = 12 - 4 = 8