How do you solve this expression? 5 square root 10^4.4× 10^-6.3 ÷ 10^-8.1

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Supposing that you should to solve the following expression `5 sqrt((10^4.4*10^(-6.3))/(10^(-8.1)))` , you need to use the negative power property suchthat:

a^(-b) = 1/(a^b)

Reasoning by analogy, you may convert each negative power such that:

`10^(-6.3) = 1/(10^6.3)`

`10^(-8.1) = 1/(10^(8.1))`

Using the conversions above yields:

`5 sqrt((10^4.4*10^(-6.3))/(10^(-8.1)))` = `5sqrt ((10^4.4*(1/(10^6.3)))/(1/(10^8.1)))` = `5sqrt ((10^4.4*10^8.1)/(10^6.3))`

You also need to use the following exponetial identity such that:

`a^x*a^y = a^(x+y)`

`a^x/a^y = a^(x-y)`

Reasoning by analogy yields:

`5 sqrt (10^(4.4+8.1-6.3)) = 5sqrt (10^6.2)`

You need to convert the square root into a power such that:

`5sqrt (10^6.2) = 5 ((10^6.2))^(1/2) => 5sqrt (10^6.2) = 5*(10)^(6.2/2)`

`5sqrt (10^6.2) = 5*10^(3.1) = 5*10^(31/10)`

Converting `10^(31/10)`  into a `n-th`  root yields:

`5sqrt (10^6.2) = 5*root(10)(10^31) = 5*10^3root(10)10 = 5000 root(10)10`

Hence, performing the simplifications and conversions above yields `5 sqrt((10^4.4*10^(-6.3))/(10^(-8.1))) = 5000 root(10)10.`

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