Question

Yoooooo could u guys help me?

Answer 1

1. 1/32
2. 32
3 (-1/32)
4 (-1/32)

Answer 2

1. 1/32
2. 32
3. -(1/32)
4. -(1/32)

Explanation:

1.

`2^-^1 \cdot 2^-^4\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^(b+c)\\2^(-1)\cdot \:2^(-4)=2^(-1-4)\\\\=2^(-1-4)\\\\=2^(-5)\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^(-b)=(1)/(a^b)\\2^(-5)=(1)/(2^5)\\\\2^5=32\\\\=(1)/(32)`

2.

`(2)/(2^-^4) \\\\\mathrm{Cancel\:the\:common\:factor:}\:2^(-4)\\=2^5\\\\2^5=32\\\\=32`

3.

`(-(1)/(2) )^3\cdot (-(1)/(2) )^2\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^(b+c)\\\left(-(1)/(2)\right)^3\left(-(1)/(2)\right)^2=\left(-(1)/(2)\right)^(3+2)\\\\=\left(-(1)/(2)\right)^5\\\\\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=-a^n,\:\quad \mathrm{if\:}n\mathrm{\:is\:odd}\\\\\left(-(1)/(2)\right)^5=-\left((1)/(2)\right)^5\\\\\mathrm{Apply\:exponent\:rule}:\quad \left((a)/(b)\right)^c=(a^c)/(b^c)\\`

`\left((1)/(2)\right)^5=(1^5)/(2^5)\\\\=-(1^5)/(2^5)\\\\=-(1)/(32)`

4.

`((-2)^-^5)/((-2)^-^1^0) \\\\\mathrm{Apply\:rule}\:a^0=1,\:a\\e \:0\\\left(\left(-2\right)^(-1)\right)^0=1\\\\=(\left(-2\right)^(-5))/(1)\\\\\left(-2\right)^(-5)=-2^(-5)\\\\=(-2^(-5))/(1)\\\\\mathrm{Apply\:the\:fraction\:rule}:\quad (-a)/(b)=-(a)/(b)\\\\=-(2^(-5))/(1)\\\\\mathrm{Apply\:rule}\:(a)/(1)=a\\=-2^(-5)\\\\\mathrm{Simplify}\:2^(-5):\quad (1)/(32)\\=-(1)/(32)`