Simplifying Radical and Fractional Expression

The question asks for the simplified value of the mathematical expression \(\left(\frac{\sqrt[3]{4913}}{\sqrt[4]{1296}}\right) \times \frac{3}{51} \times 168\). We will simplify this step-by-step.

Step 1: Calculate the Cube Root

First, find the cube root of 4913.

We look for a number whose cube is 4913. By checking or calculation, we find:

\( \sqrt[3]{4913} = 17 \)

Step 2: Calculate the Fourth Root

Next, find the fourth root of 1296.

The fourth root is the square root of the square root (\(\sqrt[4]{1296} = \sqrt{\sqrt{1296}}\)). We know \(\sqrt{1296} = 36\), and \(\sqrt{36} = 6\).

Therefore:

\( \sqrt[4]{1296} = 6 \)

Step 3: Substitute and Simplify the Expression

Now, substitute the calculated values back into the original expression:

\( \left(\frac{17}{6}\right) \times \frac{3}{51} \times 168 \)

Simplify the fraction \(\frac{3}{51}\). Since \(51 = 3 \times 17\), we get:

\( \frac{3}{51} = \frac{3}{3 \times 17} = \frac{1}{17} \)

The expression becomes:

\( \frac{17}{6} \times \frac{1}{17} \times 168 \)

Cancel out the 17s:

\( \frac{1}{6} \times 168 \)

Finally, perform the division:

\( \frac{168}{6} = 28 \)

Final Simplified Value

The simplified value of the expression is 28.