Question

find the value of a+b+c+d if the product of first 10natural numbers is written as 2^a*3^b*5^c*7^d​

Answer 1

Answer:

$\red { Value \: of \: a+b+c+d }$

$\green { = 15 }$

Step-by-step explanation:

$1,2,3,4,5,6,7,8,9 \:and \: 10 \: are \: first \: 10 \\natural \: numbers$

$Product = 1\times 2\times 3\times 4\times 5\times 6\times7\times 8\times 9\times 10$

$= 2\times 3\times 2^{2} \times 5 \times 2^{1}\times 3^{1} \times 7^{1} \times 2^{3} \times 3^{2} \times 2^{1} \times 5^{1}$

$= 2^{1+2+1+3+1} \times 3^{1+1+2}\times 5^{1+1}\times 7^{1}$

$= 2^{8} \times 3^{4} \times 5^{2} \times 7^{1}$

$= 2^{a} \times 3^{b} \times 5^{c}\times 7^{d} \:(given)$

/*Comparing both , we get */

$a = 8 , \: b = 4, \: c = 2 , \: d = 1$

Therefore.,

$\red { Value \: of \: a+b+c+d }$

$= 8+4+2+1$

$\green { = 15 }$

•••♪

Answer 2

$Answer:</p><p></p><p>\red { Value \: of \: a+b+c+d }Valueofa+b+c+d</p><p></p><p>\green { = 15 }=15</p><p></p><p>Step-by-step explanation:</p><p></p><p>\begin{gathered} 1,2,3,4,5,6,7,8,9 \:and \: 10 \: are \: first \: 10 \\natural \: numbers \end{gathered}1,2,3,4,5,6,7,8,9and10arefirst10naturalnumbers</p><p></p><p>Product = 1\times 2\times 3\times 4\times 5\times 6\times7\times 8\times 9\times 10Product=1×2×3×4×5×6×7×8×9×10</p><p></p><p>= 2\times 3\times 2^{2} \times 5 \times 2^{1}\times 3^{1} \times 7^{1} \times 2^{3} \times 3^{2} \times 2^{1} \times 5^{1}=2×3×22×5×21×31×71×23×32×21×51</p><p></p><p>= 2^{1+2+1+3+1} \times 3^{1+1+2}\times 5^{1+1}\times 7^{1}=21+2+1+3+1×31+1+2×51+1×71</p><p></p><p>= 2^{8} \times 3^{4} \times 5^{2} \times 7^{1}=28×34×52×71</p><p></p><p>= 2^{a} \times 3^{b} \times 5^{c}\times 7^{d} \:(given)=2a×3b×5c×7d(given)</p><p></p><p>/*Comparing both , we get */</p><p></p><p>a = 8 , \: b = 4, \: c = 2 , \: d = 1a=8,b=4,c=2,d=1</p><p></p><p>Therefore.,</p><p></p><p>\red { Value \: of \: a+b+c+d }Valueofa+b+c+d</p><p></p><p>= 8+4+2+1=8+4+2+1</p><p></p><p>\green { = 15 }=15</p><p></p><p>•••♪</p><p></p><p>$