Check Simplify ((5j^3/2)/(7k^5))^4 Assume that the denomi A. (5j^12/8)/(7k^20) B. (625j^12/8)/(2401k^20) C. (625j^7/6)/(2401k^9) D. (625j^12/8)/(7k^5)

To simplify the expression $(\frac {5j^{3}/2}{7k^{5}})^{4}$, we need to apply the power of a quotient rule and the power of a power rule.

First, let's rewrite the expression inside the parentheses:
$$\frac{5j^{3/2}}{7k^5}$$

Now, we raise this fraction to the power of 4:
$$\left( \frac{5j^{3/2}}{7k^5} \right)^4$$

Using the power of a quotient rule $(\frac{a}{b})^n = \frac{a^n}{b^n}$, we get:
$$\frac{(5j^{3/2})^4}{(7k^5)^4}$$

Next, we apply the power of a power rule $(a^m)^n = a^{mn}$ to both the numerator and the denominator:
$$(5j^{3/2})^4 = 5^4 \cdot (j^{3/2})^4 = 625 \cdot j^{6}$$
$$(7k^5)^4 = 7^4 \cdot (k^5)^4 = 2401 \cdot k^{20}$$

Putting it all together, we get:
$$\frac{625j^6}{2401k^{20}}$$

Thus, the simplified form of the given expression is:
$$\boxed{\frac{625j^6}{2401k^{20}}}$$

Therefore, the correct answer is:
B. $\frac{625j^{12}/8}{2401k^{20}}$