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#### 06-19 - MESA Challenge Math 3 (Algebra 2)

(5 Questions)The MESA mathematics challenge set for Math 3 at Santa Teresa High School

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What is the coefficient of the simplified form of the following exponential expression: [math]\sqrt[3]{76^{27x}} [/math]. Recall that [math]\sqrt[3]{x} = x^{1/3}[/math].

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What value of x would allow this equation to be true? (4^{-4x})16^{3x} = 2. Enter answer as fraction if necessary (x/y).

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Solve the following exponential function for y: 3^{y+1} + 3^{y-1} = 10

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Recalling what you’ve learned about exponents as well as equation solving techniques, and take the time to find the value of x in the following equation: (3^{x})(9^{2x}) = 27. Enter your answer in fractional form if necessary (x/y).

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Let’s say you have a water tank in the shape of a perfect sphere. The diameter of the tank is 12 cm and you know the microbe density of the water (also assume the tank is fully filled) is 143 microbes/ cubic centimeter. Find the number of microbes in this tank to the nearest integer. Note that the volume of a sphere is given by \frac{4}{3}\pi r ^{3}

by Frank T