Respuesta :

Given expression: [tex](256x^{16})^{1/4}[/tex].

[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n[/tex]

[tex]=256^{\frac{1}{4}}\left(x^{16}\right)^{\frac{1}{4}}[/tex]

[tex]256=4^4[/tex]

[tex]256^{\frac{1}{4}}=\left(4^4\right)^{\frac{1}{4}}=4[/tex]

[tex]\left(x^{16}\right)^{\frac{1}{4}}=x^{16\cdot \frac{1}{4}}=x^4[/tex]

[tex](256x^{16})^{1/4} =4x^4[/tex]

Therefore, correct option is B option : B.4x^4

Answer:  The correct option is (B) [tex]4x^4.[/tex]

Step-by-step explanation:  We are given to select the correct expression that is equivalent to the expression below:

[tex]E=(256x^{16})^\frac{1}{4}.[/tex]

We will be using the following properties of exponents:

[tex](i)~(a^b)^c=a^{b\times c},\\\\(ii)~(ab)^c=a^cb^c.[/tex]

We have

[tex]E\\\\=(256x^{16})^\frac{1}{4}\\\\=(4^4x^{16})^\frac{1}{4}\\\\=(4^4)^\frac{1}{4}(x^{16}^\frac{1}{4})\\\\=4^{4\times\frac{1}{4}}x^{16\times\frac{1}{4}}\\\\=4x^4.[/tex]

Therefore, the required equivalent expression is [tex]4x^4.[/tex]

Thus, (B) is the correct option.

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