To solve the exponential equation 32^x = 27^(3-5x-9), we can simplify it by first expressing both sides with the same base. Let's rewrite 27 as 3^3:
32^x = (3^3)^(3-5x-9)
Now, apply the exponent rule that states (a^b)^c = a^(b*c):
32^x = 3^(3(3-5x-9))
Now, simplify the exponent on the right side:
32^x = 3^(3(3-5x-9)) = 3^(3(3-5x-9)) = 3^(3(3-5x-9))
Now, we can equate the exponents:
x = 3(3-5x-9)
Let's solve for x:
x = 3(3-5x-9)
x = 3(3-5x-9)
x = 3(3-5x-9)
Now, distribute the 3 on the right side:
x = 9 - 15x - 27
Now, combine like terms:
16x = 9 - 27
16x = -18
Now, divide by 16:
x = -18 / 16
Simplify the fraction:
x = -9/8
So, the solution to the exponential equation 32^x = 27^(3-5x-9) is x = -9/8.