The quantity $(3^{\frac{5}{4}})(9^{\frac{3}{2}})$ can be written in the form $3^x.$ What is the value of $x$?

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10-09-2021
Mathematics

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The quantity $(3^{\frac{5}{4}})(9^{\frac{3}{2}})$ can be written in the form $3^x.$ What is the value of $x$?

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LammettHash LammettHash · Answer 1 · 2021-09-10T22:29:49+02:00

LammettHash LammettHash

10-09-2021

[tex]\left(3^{5/4}\right) \left(9^{3/2}\right) = \left(3^{5/4}\right) \left(\left(3^2\right)^{3/2}\right) = \left(3^{5/4}\right) \left(3^3\right) = 3^{5/4+3} = 3^{17/4}[/tex]

So x = 17/4.

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