? 3^x - 3^{x - 1} = 18
? 3^{x - 1}(3 - 1) = 18
? 3^{x - 1}(2) = 18
? 3^{x - 1} = 18/2
? 3^{x - 1} = 9
? 3^{x - 1} = 3²
Apply the Algebra law,
If a^X = a^Y then X will be equal to Y.
means X = Y;
? x - 1 = 2
? x = 3
Then x^x = (3)³ = 27

Given that, a^{2x + 2} = 1
Apply the algebra Law,
p⁰ = 1
? a^{2x + 2} = a⁰
Apply the algebra law
p^X = p^Y then X will be equal to Y. means X = Y;
? 2x + 2 = 0
? x = -2/2 = -1

7^8.9 ÷ (343)^1.7 x (49)^4.8 = 7^?
Apply the law of Fractional Exponents and Laws of Exponents
(a^m)(aⁿ) = a^m+n
a^m÷aⁿ=a^m?n
a^m/aⁿ=a^m?n
(a^m)ⁿ = a^mn
7^8.9 ÷ (343)^1.7 x (49)^4.8 = 7^?
? 7^8.9 ÷ (7³)^1.7 x (7²)^4.8 = 7^?
? 7^8.9 ÷ 7^5.1 x 7^9.6 = 7^?
? 7^{8.9 - 5.1 + 9.6} = 7^?
? 7^{18.5 - 5.1} = 7^?
? ? = 13.4

Given, ?10 + ? x = 4
On squaring both sides, we get
10 + ?x = 16
? ?x = 6
Now, cubic on both sides, we get
x = (6)³ = 216

Given that, (2^{4x 1/2})^? = 256
Apply the law of Fractional Exponents and Laws of Exponents
? (2²)^? = 2⁸
? 2^{2 x ?} = 2⁸
? 2 x ? = 8
? ? = 8/2 = 4