Conditional Power

Algebra Level 1

Given that 2 y − 5 x = − 8 2y - 5x = -8 , what is the value of 3 2 x 4 y \large \dfrac{32^x}{4^y} ?

2 32 2^{32} 4 8 4^8 1 6 2 16^2

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Viki Zeta by Viki Zeta , 19, India

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2 solutions

Viki Zeta
Sep 12, 2016

2 y − 5 x = − 8 ⟹ 5 x − 2 y = 8 \large 2y - 5x = -8 \\ \implies 5x - 2y = 8 3 2 x 4 y = ( ( 2 ) 5 ) x ( ( 2 ) 2 ) y = 2 5 x 2 2 y = 2 5 x − 2 y = 2 8 = ( 2 4 ) 2 = 1 6 2 \dfrac{32^x}{4^y} \large= \dfrac{((2)^5)^x}{((2)^2)^y} \\ \large= \dfrac{2^{5x}}{2^{2y}} \\ \large= 2^{5x - 2y} \\ = 2^8 \\ = (2^4)^2 \\ \large = 16^2

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Ryan Shi
Sep 19, 2016

In the answers, 2^16 = 4^8

Since it's multiple choice and the answer cannot be both, the answer has to be 1 6 2 16^2

Note: This is not the proper solution

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Yes, this should be fixed.

Jesse Nieminen - 4 years, 8 months ago

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Thanks for bringing this to our attention. I've changed one of the options from 2 16 2^{16} to 2 32 2^{32} .

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Brilliant Mathematics Staff - 4 years, 8 months ago

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