Math, asked by swetha6089, 1 year ago

A to the power 1 by a is equal to b to the power 1 by b is equal to C ^ 1 by 3 and a to the power BC + b to the power 80 + 3 to the power 80 is equal to 729 then find the value of a to the power 1 by a

Answers

Answered by SJ31
0
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Answered by amitnrw
8

A^{1/A} = 9^{1/ABC}

Step-by-step explanation:

Correction in Question

if A^{1/A} = B^{1/B} = C^{1/C}   ,  A^{BC} \times B^{AC} \times C^{AB} = 729

Let say

A^{1/A} = B^{1/B} = C^{1/C}  = k

Taking power ABC each side then

if A^{BC} = B^{AC} = C^{AB} =K^{ABC}

A^{BC} \times B^{AC} \times C^{AB} = 729\\k^{ABC} \times k^{ABC} \times k^{ABC} = 729\\( k^{ABC})^3 = 729\\( k^{ABC})^3 = 9^3\\ k^{ABC} = 9

k = 9^{1/ABC}\\A^{1/A} = 9^{1/ABC}

Hence

A^{1/A} = 9^{1/ABC}

Learn more:

(xa/xb)a+b×(xb/xc)b+c×(xc/xa)

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If A1/A = B1/B = C1/C, ABC + BAC + C AB = 729

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