Calculate the value of the expression:

$$\frac{\sqrt[3]{6859}}{\sqrt[4]{1296}} imes \frac{3}{57} imes 42 = ?$$

Question

Calculate the value of the expression:

$$\frac{\sqrt[3]{6859}}{\sqrt[4]{1296}} 	imes \frac{3}{57} 	imes 42 = ?$$

Accepted Answer

**Solution:**

1. Calculate the cube root of 6859:
   - Since $19^3 = 6859$, we have:
     $$\sqrt[3]{6859} = 19$$

2. Calculate the fourth root of 1296:
   - Note that $1296 = 6^4$ because $6^4 = 6 	imes 6 	imes 6 	imes 6 = 1296$
   - Therefore:
     $$\sqrt[4]{1296} = 6$$

3. Substitute these values into the expression:
   $$\frac{19}{6} 	imes \frac{3}{57} 	imes 42$$

4. Simplify step-by-step:
   - Simplify $\frac{3}{57}$:
     $$\frac{3}{57} = \frac{1}{19}$$ (since $3 	imes 19 = 57$)

- Now expression becomes:
     $$\frac{19}{6} 	imes \frac{1}{19} 	imes 42$$

5. Cancel $19$ in numerator and denominator:
   $$\frac{\cancel{19}}{6} 	imes \frac{1}{\cancel{19}} 	imes 42 = \frac{1}{6} 	imes 42$$

6. Multiply:
   $$\frac{1}{6} 	imes 42 = 7$$

**Answer:** $7$

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