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

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UpStudy AI · Accepted Answer

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:
$$
\frac{27}{16}
$$
The value of $$ 8u^{2}v^{3} $$ when $$ u=\frac{1}{4} $$ and $$ v=\frac{3}{2} $$ is $$ \frac{27}{16} $$.

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

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