Question

when simplified, the expression \\(\left(x^{\frac{1}{8}}\
ight)\left(x^{\frac{3}{8}}\
ight)\\) is 12. which is a possible value of x?\
\\(\bigcirc\\) 6\
\\(\bigcirc\\) 24\
\\(\bigcirc\\) 144\
\\(\bigcirc\\) 256

Explanation:

Step1: Combine exponents

When multiplying terms with the same base, add exponents:
$x^{\frac{1}{8}} \cdot x^{\frac{3}{8}} = x^{\frac{1}{8}+\frac{3}{8}} = x^{\frac{4}{8}} = x^{\frac{1}{2}}$

Step2: Set equal to 12

Equate simplified expression to 12:
$x^{\frac{1}{2}} = 12$

Step3: Solve for x

Square both sides to isolate x:
$(x^{\frac{1}{2}})^2 = 12^2$
$x = 144$

Answer:

144