Solve the following equation with a rational exponent: 2x32=16
.(1 point)
Responses
8
84
4
no solution
To solve the equation 2x^32 = 16, we need to isolate the variable x.
First, we rewrite the equation as x^32 = 8.
Then, we can take the 32nd root of both sides to eliminate the exponent.
The 32nd root of 8 is 2, so x = 2 is the solution to the equation.
Therefore, the correct response is: 2
To solve the equation 2^(x/3) = 16, we need to isolate the variable x.
First, we can rewrite 16 as a power of 2:
2^(x/3) = 2^(4)
Since the bases are the same, we can equate the exponents:
x/3 = 4
To solve for x, we can multiply both sides of the equation by 3:
3 * (x/3) = 3 * 4
x = 12
Therefore, the solution to the equation is x = 12.