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CBSE Class 7 Answered

1. evaluate ((14)^7 * (4)^7 * (25)^5 * (81)^3) / ((15)^7 * (12)^5 * (80)^3 * (7)^3)  
Asked by nitishasen10 | 22 Feb, 2019, 12:26: PM
answered-by-expert Expert Answer
begin mathsize 12px style L e t space A space equals space fraction numerator 14 to the power of 7 cross times 4 to the power of 7 cross times 25 to the power of 5 cross times 81 cubed over denominator 15 to the power of 7 cross times 12 to the power of 5 cross times 80 cubed cross times 7 cubed end fraction space end style

The above expression can be simplified , by expressing each term as power of prime numbers
 
begin mathsize 12px style fraction numerator 2 to the power of 7 cross times 7 to the power of 7 cross times 2 to the power of 14 cross times 5 to the power of 10 cross times 3 to the power of 12 over denominator 5 to the power of 7 cross times 3 to the power of 7 cross times 3 to the power of 5 cross times 2 to the power of 10 cross times 2 to the power of 12 cross times 5 cubed cross times 7 cubed end fraction space equals space fraction numerator 2 to the power of 21 cross times 3 to the power of 12 cross times 5 to the power of 10 cross times 7 to the power of 7 over denominator 2 to the power of 22 cross times 3 to the power of 12 cross times 5 cubed cross times 7 cubed end fraction space equals space 7 to the power of 4 over 2 space equals space 2401 over 2 space equals 1200.5 end style
Answered by Thiyagarajan K | 22 Feb, 2019, 02:03: PM

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