a=[a/c b/d] then apower to -1 is equals to
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Answer:
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Answer:
Given:
\text{The product of first 10 natural numbers}The product of first 10 natural numbers
\mathrm{=2^a{\times}3^b{\times}5^c{\times}7^c}=2
a
×3
b
×5
c
×7
c
\textbf{To find:}To find:
\text{The value of a+b+c+d}The value of a+b+c+d
\textbf{Solution:}Solution:
\text{Consider,}Consider,
\mathrm{1{\times}2{\times}3{\times}4{\times}5{\times}6{\times}7{\times}8{\times}9{\times}10=2^a{\times}3^b{\times}5^c{\times}7^d}1×2×3×4×5×6×7×8×9×10=2
a
×3
b
×5
c
×7
d
\mathrm{2{\times}3{\times}2^2{\times}5{\times}(2{\times}3){\times}7{\times}2^3{\times}(3{\times}3){\times}(2{\times}5)=2^a{\times}3^b{\times}5^c{\times}7^d}2×3×2
2
×5×(2×3)×7×2
3
×(3×3)×(2×5)=2
a
×3
b
×5
c
×7
d
\mathrm{2^8{\times}3^4{\times}5^2{\times}7^1=2^a{\times}3^b{\times}5^c{\times}7^d}2
8
×3
4
×5
2
×7
1
=2
a
×3
b
×5
c
×7
d
\text{Equating powers, we get}Equating powers, we gea=8,b=4,c=2,d=1}a=8,b=4,c=2,d=1
Now
a+b+c+d}a+b+c+d
{=8+4+2+1}=8+4+2+1
{=15}=15
{The value of a+b+c+d is 15}The value of a+b+c+d is 15