It looks like the equation is supposed to read
3⁴ˣ ⁻ ⁵ = (1/27)²ˣ ⁺ ¹⁰
Recall that 3³ = 27, so 1/27 = 3⁻³ :
3⁴ˣ ⁻ ⁵ = (3⁻³)²ˣ ⁺ ¹⁰
Distribute the exponent on the right side:
3⁴ˣ ⁻ ⁵ = 3 ⁻⁶ˣ ⁻ ³⁰
The exponents must be equal for this equation to hold, so
4x - 5 = -6x - 30
Solve for x :
10x = -25
x = -25/10 = -5/2
