Modulus function

If $a>0$ , then  $\sqrt{a^2}=a$ .

• Always true

• Sometimes true

• Never true

If $a<0$ , then  $\sqrt{a^2}=a$ .

• Always true

• Sometimes true

• Never true

For any real number  $a$ , $\left|a\right|^2=a^2$ .

• Always true.

• Sometimes true.

• Never true.

For any real number  $a$ , $\left|a\right|^3=a^3$ .

• Always true.

• Sometimes true.

• Never true.

For any real number  $a$ , $\left|a\right|^4=a^4$ .

• Always true.

• Sometimes true.

• Never true.

 $\left|a\right|^k=a^k$  , where  $k$ is an even number and  $a$  is a positive integer.

• Always true.

• Sometimes true.

• Never true.

 $\left|a\right|^k=a^k$  , where  $k$ is an odd number and  $a$  is a negative integer.

• Always true.

• Sometimes true.

• Never true.

 $\left|a\right|^n=a^n$ , where  $n$   is a positive integer and  $a$  is a real number

• Always true.

• Sometimes true.

• Never true.

 $\left|a+b\right|=\left|a\right|+\left|b\right|$ , where  $a$  and  $b$  are real numbers.

• Always true.

• Sometimes true.

• Never true.

 $\left|a-b\right|=\left|a\right|-\left|b\right|$ , where  $a$  and  $b$  are real numbers.

• Always true.

• Sometimes true.

• Never true.