To simplify an expression is to reduce the expression to the lowest term. The solution to [tex]((6^2 \times 10) + \frac{\sqrt{(5000*3) - 600)}}{ 4!} * 4 ) - \log(1 * 10^{11})[/tex] is 370
Given that:
[tex]((6^2 \times 10) + \frac{\sqrt{(5000*3) - 600)}}{ 4!} * 4 ) - \log(1 * 10^{11})[/tex]
First, we evaluate all exponents
[tex]((36 \times 10) + \frac{\sqrt{(5000*3) - 600)}}{ 4!} * 4 ) - \log(1 * 10^{11})[/tex]
Evaluate the factorials
[tex]((36 \times 10) + \frac{\sqrt{(5000*3) - 600)}}{4\times 3 \times 2 \times 1} * 4 ) - \log(1 * 10^{11})[/tex]
Evaluate the multiplications/divisions
[tex]((360) + \frac{\sqrt{(15000) - 600)}}{24} * 4 ) - \log(10^{11})[/tex]
Evaluate the multiplications/divisions
[tex]((360) + \frac{\sqrt{(15000) - 600)}}{6} ) - \log(10^{11})[/tex]
Apply law of logarithm
[tex]((360) + \frac{\sqrt{(15000) - 600)}}{6} ) - 10\log(10)[/tex]
[tex]\log(10) = 1[/tex]
So, we have:
[tex]((360) + \frac{\sqrt{(15000) - 600)}}{6} ) - 10[/tex]
Subtract
[tex]((360) + \frac{\sqrt{14400)}}{6} ) - 10[/tex]
Evaluate the square roots
[tex]((360) + \frac{120}{6} ) - 10[/tex]
Evaluate the division
[tex]((360) + 20 ) - 10[/tex]
Remove all brackets
[tex]360 + 20 - 10[/tex]
Simplify
[tex]370[/tex]
Hence:
[tex]((6^2 \times 10) + \frac{\sqrt{(5000*3) - 600)}}{ 4!} * 4 ) - \log(1 * 10^{11}) = 370[/tex]
Read more about simplification at:
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