when simplified, the expression $(x^{\frac{1}{8}})(x^{\frac{3}{8}})$ is 12. which is a possible value of…

Answer:

C. 144

Explanation:

Step1: Use exponent - rule

When multiplying two terms with the same base (a^m\times a^n=a^{m + n}), so (x^{\frac{1}{8}}\times x^{\frac{3}{8}}=x^{\frac{1 + 3}{8}}=x^{\frac{4}{8}}=x^{\frac{1}{2}}).

Step2: Set up the equation

We have the equation (x^{\frac{1}{2}} = 12).

Step3: Solve for (x)

Square both sides of the equation ((x^{\frac{1}{2}})^2=12^2). According to the power - of - a - power rule ((a^m)^n=a^{mn}), so (x = 144).