What value of a will make ((12x^a)/(4x^5))^3 = 27x^12?

2 Answers
Apr 30, 2017

To find a we have to perform ((12x^a)/(4x^5))^3 by applying some power properties then solve the given equation.
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color(blue)(((12x^a)/(4x^5))^3
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=(12x^a)^3/(4x^5)^3
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=(12^3xx(x^a)^3)/(4^3xx(x^5)^3
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=(1728xxx^(3a))/(64xxx^15)
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=1728/64xxx^(3a)/x^15
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color(blue)(=27xxx^(3a-15)
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Now let us solve the given equation:
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((12x^a)/(4x^5))^3=27x^12
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rArrcolor(blue)(cancel27xxx^(3a-15))=cancel27x^12
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rArrx^(3a-15)=x^12
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rArr3a-15=12
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rArr3a=12+15
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rArr3a=27rArra=27/3
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Therefore," "a=9

Apr 30, 2017

a=9

Explanation:

((12x^a)/(4x^5))^3 =27 x^12 Multiplying by (4x^5)^3 in both sides

we get , (12x^a)^3 =27*x^12 *64*x^15 or

12^3 x^(3a) = 27*64* x^27 or x^(3a)= 27*64*x^27/12^3or

x^(3a) = x^27 :. 3a =27 or a =9 [Ans]