Remember
![x^ \frac{m}{n} = \sqrt[n]{x^m}](https://tex.z-dn.net/?f=x%5E%20%5Cfrac%7Bm%7D%7Bn%7D%20%3D%20%5Csqrt%5Bn%5D%7Bx%5Em%7D%20)
and
and
(x^m)^n=x^(mn)
so
![((7x^3)(y^2))^ \frac{2}{7} = \sqrt[7]{((7x^3)(y^2))^2}](https://tex.z-dn.net/?f=%20%28%287x%5E3%29%28y%5E2%29%29%5E%20%5Cfrac%7B2%7D%7B7%7D%20%3D%20%5Csqrt%5B7%5D%7B%28%287x%5E3%29%28y%5E2%29%29%5E2%7D%20)
=
![\sqrt[7]{((7x^3)^2(y^2)^2)}](https://tex.z-dn.net/?f=%20%5Csqrt%5B7%5D%7B%28%287x%5E3%29%5E2%28y%5E2%29%5E2%29%7D%20)
=
![\sqrt[7]{((7^2x^6)(y^4))}](https://tex.z-dn.net/?f=%20%5Csqrt%5B7%5D%7B%28%287%5E2x%5E6%29%28y%5E4%29%29%7D%20)
=
![\sqrt[7]{((49x^6)(y^4))}](https://tex.z-dn.net/?f=%20%5Csqrt%5B7%5D%7B%28%2849x%5E6%29%28y%5E4%29%29%7D%20)
=
![\sqrt[7]{49x^6y^4}](https://tex.z-dn.net/?f=%20%5Csqrt%5B7%5D%7B49x%5E6y%5E4%7D%20)
and
and
(x^m)^n=x^(mn)
so
Simplify the expression: 3(3 + 7b)
2 answers:
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Answer:
A. 183 meters
Step-by-step explanation:
Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B. About how much farther is it to drive than to walk directly from building A to building B? Round to the nearest whole number. A) 183 meters B) 250 meters C) 366 meters D) 683 meters
Find distance BC
Cos (60°)=BC / AB (Adjacent divided by the hypotenuse)
Cos (60°)=1/2
BC=a
AB=500
Cos (60°)=BC / AB
1/2=a/500
1/2 * 500=a
250=a
a=250m
Find distance AC
Sin(60°)=AC/AB (opposite side divided by hypotenuse)
Sin(60°)=√3/2
AC=b
AB=500
Sin(60°)=AC/AB
√3/2=b/500
√3/2 * 500=b
250√3=b
b=433m
Distance AC and BC=AC+BC
433m+250m=683m
Subtract the distance AB from AC+BC
= 683m - 500m
=183m
Answer is A. 183 meters
