So,
In order to simplify a fraction, we have to factor both the numerator and the denominator.
![\frac{420}{15} --\ \textgreater \ \frac{2*2*3*5*7}{3*5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B420%7D%7B15%7D%20--%5C%20%5Ctextgreater%20%5C%20%20%20%5Cfrac%7B2%2A2%2A3%2A5%2A7%7D%7B3%2A5%7D%20)
Cross out ones.
Answer:
4^8
Step-by-step explanation:
Because both expressions have the same base, we can add the exponents to simplify the expression:
![4^5*4^3 = 4^{5+3} = 4^8](https://tex.z-dn.net/?f=4%5E5%2A4%5E3%20%3D%204%5E%7B5%2B3%7D%20%3D%204%5E8)
Answer:
Step-by-step explanation:
pi^3 is about 30. (3 * 3 * 3 get's you to 27. The 0.14 will make a bit more)
pi^2 is about 10 (3^2 = 9. You need only get an approximate answer)
pi/4 = about 0.75 I'm using 3 to be the value of pi. That's close enough to get an answer.
pi/8 = 3/8 which is about 0.375 which is the smallest one.
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Answer: 3rd one down.
Answer:
<h2>4.46</h2>
Step-by-step explanation:
The formula of a distance between two points:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
We have (-3, 1) and (-1, 5). Substitute:
![d=\sqrt{(-1-(-3))^2+(5-1)^2}=\sqrt{2^2+4^2}=\sqrt{4+16}=\sqrt{20}\\\\=\sqrt{4\cdot5}=\sqrt4\cdot\sqrt5=2\sqrt5\approx2\cdot2.23=4.46](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-1-%28-3%29%29%5E2%2B%285-1%29%5E2%7D%3D%5Csqrt%7B2%5E2%2B4%5E2%7D%3D%5Csqrt%7B4%2B16%7D%3D%5Csqrt%7B20%7D%5C%5C%5C%5C%3D%5Csqrt%7B4%5Ccdot5%7D%3D%5Csqrt4%5Ccdot%5Csqrt5%3D2%5Csqrt5%5Capprox2%5Ccdot2.23%3D4.46)