Question

Select the simplification that accurately explains the following statement.

Answer 1

Answer:

Option (b) is correct.

$(2^\frac{1}{4} )^4=2^\frac{1}{4} \times 2^\frac{1}{4}\times 2^\frac{1}{4}\times 2^\frac{1}{4}=2^{(\frac{1}{4}+ \frac{1}{4}+ \frac{1}{4}+ \frac{1}{4} )}=2^{1}=2$

Step-by-step explanation:

Given: $(2^\frac{1}{4} )^4$

We have too choose the correct simplification for the given statement.

Consider $(2^\frac{1}{4} )^4$

Using property of exponents, $(a^m)^n=a^m\times a^m\times a^m\times ....\times (n\ times)$

We have,

$(2^\frac{1}{4} )^4=2^\frac{1}{4} \times 2^\frac{1}{4}\times 2^\frac{1}{4}\times 2^\frac{1}{4}$

Again applying property of exponents  $a^m\times a^m=a^{n+m}$

We have,

$(2^\frac{1}{4} )^4=2^{(\frac{1}{4}+ \frac{1}{4}+ \frac{1}{4}+ \frac{1}{4} )}$

Simplify, we have,

$(2^\frac{1}{4} )^4=2^{\frac{4}{4}}$

we get,

$(2^\frac{1}{4} )^4=2^{1}=2$

Thus, $(2^\frac{1}{4} )^4=2$

Option (b) is correct.

   

Answer 2

$(2^{1/4})^4=2^{1/4}.2^{1/4}.2^{1/4}.2^{1/4}=2^{1/4+1/4+1/4+1/4}=2^{4/4}=2$

There you use these properties:

1) definition of the power=> $(2^{1/4})^4 =2^{1/4}.2^{1/4}.2^{1/4}.2^1/4}$

2) multiplication of powers with the same base:

$a^n.a^m.a^p.a^q=a^{n+m+p+q}$

3) sum of fractions: 1/4 +1/4 +1/4 +1/4 = 4/4

4) simplification of fractions: 4/4 = 1