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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?

May 2, 2020

#1
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Hi andrewstanells,

I'm not sure if my answer is right, but here's my solution anyways:

$$3^\frac{5}{4}=3^\frac{5}{4}$$

$$9^{\frac{3}{2}}=(3^2)^{\frac{3}{2}}=3^3$$

So, $$3^{\frac{5}{4}}\cdot3^3=3^{{\frac{5}{4}}+3}=\boxed{3^\frac{17}{4}}$$

So, $$\boxed{x=\frac{17}{4}}$$

I hope this helped you!

:)

May 2, 2020

#1
+457
+2

Hi andrewstanells,

I'm not sure if my answer is right, but here's my solution anyways:

$$3^\frac{5}{4}=3^\frac{5}{4}$$

$$9^{\frac{3}{2}}=(3^2)^{\frac{3}{2}}=3^3$$

So, $$3^{\frac{5}{4}}\cdot3^3=3^{{\frac{5}{4}}+3}=\boxed{3^\frac{17}{4}}$$

So, $$\boxed{x=\frac{17}{4}}$$

I hope this helped you!

:)

#2
+62
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it is right, thank you lokiisnotdead! :)

andrewstanells  May 2, 2020
edited by andrewstanells  May 2, 2020
#3
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you're welcome andewstanells! :)

#4
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THX, guys!!!