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If 1176 = `2^Axx3^Bxx7^C,` Find the Values of A, B and C. Hence, Compute the Value of `2^Axx3^Bxx7^-c` as a Fraction. - Mathematics

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ConceptLaws of Exponents for Real Numbers

Question

If 1176 = `2^axx3^bxx7^c,` find the values of a, b and c. Hence, compute the value of `2^axx3^bxx7^-c` as a fraction.

Solution

First find the prime factorisation of 1176.

It can be observed that 1176 can be written as `2^3xx3^1xx7^2`

`1176=2^a3^b7^c=2^3 3^1 7^2`

So, a = 3, b = 1 and c = 2.

Therefore, the value of `2^a xx3^bxx76-c` is `2^3xx3^1xx7^-2=8xx3xx1/49=24/49`

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Solution If 1176 = `2^Axx3^Bxx7^C,` Find the Values of A, B and C. Hence, Compute the Value of `2^Axx3^Bxx7^-c` as a Fraction. Concept: Laws of Exponents for Real Numbers.
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