Principle: Law of Exponents - Combination of product to a power & power to a power. The first is when raising a product of two integers to a power, the power is distributed to each factor. In equation it is,
(xy)^a = (x^a)(y^a)
The latter is when raising the base with a power to a power, the base will remain the same and the powers will be multiplied. In equation it is,
(x^a)(x^b) = x^ab
Check:
f(x) = 5*(16)^.33x = 5*(8*2)^0.33x = 5*(8^0.33x)(2^0.33x) = 5*(2^x)*(2^0.33x) = 5*(2^1.33x)
f(x) = 2.3*(8^0.5x) = 2.3*(4*2)^0.5x = 2.3*(2^x)(2^0.5x) = 2.3*(2^1.5x)
f(x) = 81^0.25x = 3^x
f(x) = 0.75*(9*3)^0.5x = 0.75*(3^x)*(3^0.5x) = 0.75*3^1.5x
f(x) = 24^0.33x = (8*3)^0.33x = (2^x)*(3^0.33x)
Therefore, the answer is third equation.
<em>ANSWER: f(x) = 81^0.25x = 3^x</em>
Answer:
120°; 240°
Step-by-step explanation:
Let's first solve for 
: 
At this point it's just a matter of drawing a circle, and mark where the angle is(please excuse my paint skills, but free hand drawing would be even worse). Red line, is 
on the cosines, and both the green and blue lines are valid solutions. The green line is a quarter of a circle, plus 30°, or 120°. The blue one is 3/4 of a circle, minus 30 degrees, or 240°.
8x-19=-3x-41
+3x +3x
11x-19=-41
+19 +19
11x=-22
÷11 ÷11
x=-2
Answer:
Since 6 lemons are used to make 4 cups of lemonade, then are used 
of lemon per cup of lemonade, or are make 
cups of lemonade per lemon.
2(4x - 9) =
2 * 4x - 2 * 9 =
8x - 18
Hope this helps!!
~Kiwi
