Cool Algebra problem

Algebra Level 2

If 3 a − b = 12 3a - b = 12 , what is the value of 8 a 2 b \dfrac{8^{a}}{2^{b}} ?

This problem A part of this My problems set .

4 4 \text{4}^{4} 2 12 \text{2}^{12} The value cannot be determined from the information given. 8 2 \text{8}^{2}

Matin Naseri by Matin Naseri , 17, Afghanistan

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3 solutions

Chew-Seong Cheong
Feb 13, 2018

8 a 2 b = 2 3 a 2 b = 2 3 a − b = 2 12 \dfrac {8^a}{2^b} = \dfrac {2^{3a}}{2^b} = 2^{\color{#3D99F6}3a-b} = \boxed{2^{\color{#3D99F6}12}} . It is given that 3 a − b = 12 \color{#3D99F6} 3a-b= 12 .

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Mahdi Raza
Jun 8, 2020

Given 3 a − b = 12 3a-b = 12 , 8 a 2 b = 2 3 a 2 b = 2 3 a − b = 2 12 \dfrac{8^a}{2^b} = \dfrac{2^{3a}}{2^b} = 2^{3a-b} = 2^{12}

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3 a − b = 12 ⟹ a = b + 12 3 3a-b=12 \implies a=\dfrac{b+12}{3}

8 a 2 b = 8 b + 12 3 2 b = 2 b + 12 2 b = 2 12 \dfrac{8^a}{2^b} =\dfrac{8^{\frac{b+12}{3}}}{2^b}=\dfrac{2^{b+12}}{2^b}=\boxed{2^{12}}

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