Question

Which expression is equivalent to (256x^16)^1/4 A.4x^2 B.4x^4 C. 64x^2 D. 64x^4

Answer 1

Given expression: $(256x^{16})^{1/4}$.

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

$=256^{\frac{1}{4}}\left(x^{16}\right)^{\frac{1}{4}}$

$256=4^4$

$256^{\frac{1}{4}}=\left(4^4\right)^{\frac{1}{4}}=4$

$\left(x^{16}\right)^{\frac{1}{4}}=x^{16\cdot \frac{1}{4}}=x^4$

$(256x^{16})^{1/4} =4x^4$

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

Answer 2

Answer:  The correct option is (B) $4x^4.$

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

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

We will be using the following properties of exponents:

$(i)~(a^b)^c=a^{b\times c},\\\\(ii)~(ab)^c=a^cb^c.$

We have

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

Therefore, the required equivalent expression is $4x^4.$

Thus, (B) is the correct option.