Answer:
![=536870912](https://tex.z-dn.net/?f=%3D536870912)
Step-by-step explanation:
![\frac{\left(2^3\right)^{10}\cdot \:2^{-8}}{2^{-7}}\\\mathrm{Cancel\:}\frac{\left(2^3\right)^{10}\cdot \:2^{-8}}{2^{-7}}:\quad \frac{\left(2^3\right)^{10}}{2}\\\frac{\left(2^3\right)^{10}\cdot \:2^{-8}}{2^{-7}}\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=\frac{1}{x^{b-a}}\\\frac{2^{-8}}{2^{-7}}=\frac{1}{2^{-7-\left(-8\right)}}\\=\frac{\left(2^3\right)^{10}}{2^{-7-\left(-8\right)}}\\\mathrm{Subtract\:the\:numbers:}\:-7-\left(-8\right)=\\=\frac{\left(2^3\right)^{10}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cleft%282%5E3%5Cright%29%5E%7B10%7D%5Ccdot%20%5C%3A2%5E%7B-8%7D%7D%7B2%5E%7B-7%7D%7D%5C%5C%5Cmathrm%7BCancel%5C%3A%7D%5Cfrac%7B%5Cleft%282%5E3%5Cright%29%5E%7B10%7D%5Ccdot%20%5C%3A2%5E%7B-8%7D%7D%7B2%5E%7B-7%7D%7D%3A%5Cquad%20%5Cfrac%7B%5Cleft%282%5E3%5Cright%29%5E%7B10%7D%7D%7B2%7D%5C%5C%5Cfrac%7B%5Cleft%282%5E3%5Cright%29%5E%7B10%7D%5Ccdot%20%5C%3A2%5E%7B-8%7D%7D%7B2%5E%7B-7%7D%7D%5C%5C%5Cmathrm%7BApply%5C%3Aexponent%5C%3Arule%7D%3A%5Cquad%20%5Cfrac%7Bx%5Ea%7D%7Bx%5Eb%7D%3D%5Cfrac%7B1%7D%7Bx%5E%7Bb-a%7D%7D%5C%5C%5Cfrac%7B2%5E%7B-8%7D%7D%7B2%5E%7B-7%7D%7D%3D%5Cfrac%7B1%7D%7B2%5E%7B-7-%5Cleft%28-8%5Cright%29%7D%7D%5C%5C%3D%5Cfrac%7B%5Cleft%282%5E3%5Cright%29%5E%7B10%7D%7D%7B2%5E%7B-7-%5Cleft%28-8%5Cright%29%7D%7D%5C%5C%5Cmathrm%7BSubtract%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A-7-%5Cleft%28-8%5Cright%29%3D%5C%5C%3D%5Cfrac%7B%5Cleft%282%5E3%5Cright%29%5E%7B10%7D%7D%7B2%7D)
![\mathrm{Simplify\:}\left(2^3\right)^{10}:\quad 2^{30}\\\left(2^3\right)^{10}\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}\\=2^{3\cdot \:10}\\\mathrm{Multiply\:the\:numbers:}\:3\cdot \:10=30\\=2^{30}\\=\frac{2^{30}}{2}\\\mathrm{Cancel\:the\:common\:factor:}\:2\\=2^{29}\\2^{29}=536870912\\=536870912](https://tex.z-dn.net/?f=%5Cmathrm%7BSimplify%5C%3A%7D%5Cleft%282%5E3%5Cright%29%5E%7B10%7D%3A%5Cquad%202%5E%7B30%7D%5C%5C%5Cleft%282%5E3%5Cright%29%5E%7B10%7D%5C%5C%5Cmathrm%7BApply%5C%3Aexponent%5C%3Arule%7D%3A%5Cquad%20%5Cleft%28a%5Eb%5Cright%29%5Ec%3Da%5E%7Bbc%7D%5C%5C%3D2%5E%7B3%5Ccdot%20%5C%3A10%7D%5C%5C%5Cmathrm%7BMultiply%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A3%5Ccdot%20%5C%3A10%3D30%5C%5C%3D2%5E%7B30%7D%5C%5C%3D%5Cfrac%7B2%5E%7B30%7D%7D%7B2%7D%5C%5C%5Cmathrm%7BCancel%5C%3Athe%5C%3Acommon%5C%3Afactor%3A%7D%5C%3A2%5C%5C%3D2%5E%7B29%7D%5C%5C2%5E%7B29%7D%3D536870912%5C%5C%3D536870912)
The decimal equivalent of 3/7 rounded to the nearest hundreds is 0.428
Answer:
b = 60
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
b² + 63² = 87²
b² + 3969 = 7569 ( subtract 3969 from both sides )
b² = 3600 ( take the square root of both sides )
b =
= 60
Answer:
35
Step-by-step explanation:
distance formula: √(x2-x1)^2+(y2-y1)^2
√(3-3)^2+(-5-0)^2= √25= 5
√(-4-3)^2+(-0-0)^2= √49= 7
7(5)= 35
<span>Use inductive reasoning</span>