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# Which exponential functions have been simplified correctly check all that apply Download jpg

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Principle: the Law of Exponents - Combination of a product to a power, and the power of a power. The first is when raising a product of two integers to a power, the power is distributed to each factor. In the equation is,(xy)^a = (x^) (y^a)The last is the time to lift the base with a power to a power of the base remains the same and the powers are multiplied. In the equation is, (x^a)(x^b) = x^abCheck:f(x) = 5*(16)^.33x = 5*(8*2)^0.33 x = 5*(8^0.33 x)(2^0.33 x) = 5*(2^x)*(2^0.33 x) = 5*(2^1.33 x)f(x) = 2.3*(8^0.5 x) = 2.3*(4*2)^0.5 x = 2.3*(2^x)(2^0.5 x) = 2.3*(2^1.5 x)f(x) = 81^0.25 x = 3^xf(x) = 0.75*(9*3)^0.5 x = 0.75*(3^x)*(3^0.5 x) = 0.75*3^1.5 xf(x) = 24^0.33 x = (8*3)^0.33 x = (2^x)*(3^0.33 x)therefore, the answer is the third equation.ANSWER: f(x) = 81^0.25 x = 3^x