Put the simplified expressions in order on the number line from least to greatest.
* 2^6-2^4/2^2
* (-2)^-8 . (-2)^11
* (1/2)^-3
*1/4^-2
To simplify the expressions, we evaluate the exponents first.
1. 2^6 = 64, 2^4 = 16, and 2^2 = 4. So, 2^6 - 2^4/2^2 = 64 - 16/4 = 64 - 4 = 60.
2. (-2)^-8 = 1/(-2)^8 = 1/256, and (-2)^11 = -2048. Therefore, (-2)^-8 . (-2)^11 = 1/256 * -2048 = -8.
3. (1/2)^-3 = 2^3 = 8.
4. (1/4)^-2 = 4^2 = 16.
Arranging the expressions from least to greatest on the number line:
1/256 = -8 < 16 < 60 < 8
are you sure
Apologies, I made an error in my response. Let's correct it.
To simplify the expressions:
1. 2^6 - 2^4 / 2^2 = 64 - 16 / 4
= 64 - 4
= 60
2. (-2)^-8 * (-2)^11 = 1 / (-2)^8 * (-2)^11
= 1 / (1 / (-2)^8 * (-2)^11)
= 1 / (1 / 256 * (-2048))
= 1 / (1 / 256 * -2048)
= 1 / (-2048/256)
= 1 / (-8)
= -1/8
3. (1/2)^-3 = 2^3
= 8
4. (1/4)^-2 = 4^2
= 16
Arranging the expressions from least to greatest on the number line:
-1/8 < 8 < 16 < 60