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# Difficult exponents

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Write (2√3)(5√27^3) as a single exponent

Guest Apr 23, 2017
#1
+93691
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Write (2√3)(5√27^3) as a single exponent

$$(2\sqrt3)(5(\sqrt{27})^3)\\ =(2\sqrt3)(5(\sqrt{9*3})^3)\\ =(2\sqrt3)(5(3\sqrt{3})^3)\\ =(2\sqrt3)(5(3^3(\sqrt{3})^3)\\ =(2\sqrt3)(5(3^3(3\sqrt{3}))\\ =2*\sqrt3*5*3^3*3\sqrt{3}\\ =2*5*3^3*3\sqrt{3}*\sqrt3\\ =10*3^3*3*3\\ =10*3^5\\$$

Melody  Apr 23, 2017
#2
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Could you put that into grade 11 terms?

Guest Apr 23, 2017
#3
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n = 10 * 3^(1/2) * 27^(3/2) = 10 * 3^(1/2) * 3^(9/2) = 10 * 3^(10/2) = 10 * 3^5

Guest Apr 23, 2017