Question Evaluate \( 8 u^{2} v^{3} \) when \( u=\frac{1}{4} \) and \( v=\frac{3}{2} \)

1. Substitute the given values into the expression: \[ 8u^{2}v^{3} = 8\left(\frac{1}{4}\right)^2\left(\frac{3}{2}\right)^3 \] 2. Compute \(\left(\frac{1}{4}\right)^2\): \[ \left(\frac{1}{4}\right)^2 = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} \] 3. Compute \(\left(\frac{3}{2}\right)^3\): \[ \left(\frac{3}{2}\right)^3 = \frac{3}{2} \times \frac{3}{2} \times \frac{3}{2} = \frac{27}{8} \] 4. Substitute these results back into the expression: \[ 8u^{2}v^{3} = 8 \times \frac{1}{16} \times \frac{27}{8} \] 5. Simplify the expression: - Multiply \(8\) by \(\frac{1}{16}\): \[ 8 \times \frac{1}{16} = \frac{8}{16} = \frac{1}{2} \] - Then multiply by \(\frac{27}{8}\): \[ \frac{1}{2} \times \frac{27}{8} = \frac{27}{16} \] Final answer: \[ \frac{27}{16} \]