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

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.

8 0

3 years ago

Read 2 more answers

Please Help!!!! 20 Points!!!!

Mekhanik [1.2K]

Answer:

C and D

Step-by-step explanation:

We can see that the base of the bigger triangle is 6. Based on the straight sides adjacent to the hypotenuse, the bigger one's height is 6 and the smaller one's is 3. This means that the smaller one is half the size of the bigger one. This means that if the bigger base is 6, the smaller one is 3. Since it is 3, we move 3 spaces left from point Z to get point Y. If you moved 3 spaces left, it would be (-5,2). You can also move 3 spaces right and then your Y point would be at (1,2) so C and D are the 2 possible answers.

4 0

3 years ago