which expression is equivalent to $(256x^{16})^{\frac{1}{4}}$?\n$4x^{2}$\n$4x^{4}$\n$64x^{2}$\n$64x^{4}$

Explanation:

Step1: Apply power - of - a - product rule

Use the rule $(ab)^n=a^n\times b^n$. So, $(256x^{16})^{\frac{1}{4}} = 256^{\frac{1}{4}}\times(x^{16})^{\frac{1}{4}}$.

Step2: Calculate $256^{\frac{1}{4}}$

Find the fourth - root of 256. Since $4^4 = 256$, then $256^{\frac{1}{4}}=4$.

Step3: Calculate $(x^{16})^{\frac{1}{4}}$

Use the power - of - a - power rule $(a^m)^n=a^{mn}$. So, $(x^{16})^{\frac{1}{4}}=x^{16\times\frac{1}{4}}=x^4$.

Step4: Combine the results

$256^{\frac{1}{4}}\times(x^{16})^{\frac{1}{4}}=4x^4$.

Answer:

B. $4x^4$