Needing help with exponential function problems?

1 4^x * 2^(x^2)=16^2

(2^2)^x * 2^(x^2) = (2^4)^2............expressing 4 and 16 as powers of 2

2^(2x) * 2^(x^2) = 2^(8)

2^(2x + x^2) = 2^(8) ................ law of indices for multiplication

2x + x^2 = 8 ...............powers of the same base

x^2 + 2x - 8 = 0

(x + 4)(x - 2) = 0.................factorising

x = 2, - 4

2 3^(x^3)=9x ....... Is this suppose to be 3^(x^3) = 9^x?

3^(x^3) = (3^2)^x .........expressing 9 as powers of 3

3^(x^3) = 3^(2x)

x^3 = 2x

x^3 - 2x = 0

x ( x^2 - 2) = 0

x = 0, +/-sqrt(2)

3 8^(-x+14)=16^x

(2^3)^(-x + 14) = (2^4)^x ................ 8 = 2^3, 16 = 2^4

2^(-3x + 42) = 2^4x ................ power of power rule of exponents

- 3x + 42 = 4x ........................ If a^m = a^n, then m = n

42 = 7x

x = 6

4 e^x=e^(3x+8)

x = 3x + 8....................... If a^m = a^n, then m = n

- 2x = 8

x = - 4

Hope I made your day