SOLUTION
The given expression is:
![-5\sqrt[]{147\times r^{13}\times s^8}](https://tex.z-dn.net/?f=-5%5Csqrt%5B%5D%7B147%5Ctimes%20r%5E%7B13%7D%5Ctimes%20s%5E8%7D)
Rewrite the expression
![-5\sqrt[]{49\times3\times r^{12}\times r^1\times s^{4\times2}}](https://tex.z-dn.net/?f=-5%5Csqrt%5B%5D%7B49%5Ctimes3%5Ctimes%20r%5E%7B12%7D%5Ctimes%20r%5E1%5Ctimes%20s%5E%7B4%5Ctimes2%7D%7D)
This further give
![\begin{gathered} -5\sqrt[]{49\times3\times(r^6)^2\times r^1\times(s^4)^2} \\ =-5\times7\times r^6\times s^4\sqrt[]{3\times r} \\ =-35r^6s^4\sqrt[]{3r} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20-5%5Csqrt%5B%5D%7B49%5Ctimes3%5Ctimes%28r%5E6%29%5E2%5Ctimes%20r%5E1%5Ctimes%28s%5E4%29%5E2%7D%20%5C%5C%20%3D-5%5Ctimes7%5Ctimes%20r%5E6%5Ctimes%20s%5E4%5Csqrt%5B%5D%7B3%5Ctimes%20r%7D%20%5C%5C%20%3D-35r%5E6s%5E4%5Csqrt%5B%5D%7B3r%7D%20%5Cend%7Bgathered%7D)
Therefore, the solution is
![-35r^6s^4\sqrt[]{3r}](https://tex.z-dn.net/?f=-35r%5E6s%5E4%5Csqrt%5B%5D%7B3r%7D)
Answer:
f(-4) = -2
Step-by-step explanation:
To find f(-4) use the "piece" of the function rule defined for x < -3 (because -4 is less than -3). That part of the rule says the output (range) value is x + 2, so f(-4) = -4 + 2 = -2.
Perpendicular lines have slopes that are negative reciprocals of each other, that is, if one slope is a/b, the other slope is -b/a
the given line 3x-4y=24, 4y=3x-24, y=3/4x-6 has a slope of 3/4, so the slope of the perpendicular line has a slope of -4/3
y=(-4/3)x+b, b can be any number.
<span>a³-b³=(a-b)(a²+ab+b²)
64x⁶ - 27
64 = 4³,
x⁶ = (x²)³
27 = 3³
</span>64x⁶ - 27 = 4³(x²)³ -3³ = (4x²)³ -3³. Now, we can use a formula where a=4x², b=3
(4x²)³ -3³ = (4x² -3)((4x²)² +4x²*3 + 3²) = (4x² -3)(16x⁴ +12x² + 9)
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Answer: </span>64x⁶ - 27= (4x² -3)(16x⁴ +12x² + 9) <span>
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