Answer:
n = -3/2
Step-by-step explanation:
1/4 * sqrt(2) = 2^n
We need to rewrite all the terms so that they are powers of 2
1/4 = 1/2^2 = 2^-2 because if it is in the denominator it is a negative power
sqrt (2) = 2^1/2
Rewriting the left hand side
2^-2 * 2^1/2 = 2^n
When multiplying the same base, we can add the exponents x^a * x^b = x^(a+b)
2^(-2+1/2) = 2^n
Getting a common denominator in the exponent
2^(-4/2+1/2) = 2^n
2^(-3/2) = 2^n
When the bases are the same, the exponents have to be the same
x^(a) = x^b means a=b
-3/2 = n
