= 1.

   = (256)^0.25

   = (256)^(25/100)

   = (256)^(1/4)

   = (4⁴)^(1/4)

   = 4^4(1/4)

   = 4¹

   = 4

   = (25)^(3/2)

   = (5²)^(3/2)

   = (5)^{2 x (3/2)}

   = 5³

   = 125.

Then, (17)^{3.5 + x} = 17⁸.

∴ 3.5 + x = 8

⟹ x = (8 - 3.5)

⟹ x = 4.5

   = (3 + 2√2) + (3 - 2√2) - 2

   = 4.

? = ?(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

? = [ (11)³ x (6)² ] x 1/4³
? = [ 11³ x 6² ] x 1/4³
Solve the equation by algebra law.
?= [ 1331 x 36 ] x 1/64 =1331 x 36 / 64
? = 748.6875