An example should help :-
Simplify sqrt 20:-
sqrt 20 = sqrt (4 * 5) = sqrt 4 * sqrt5 = 2 sqrt5
cube root of 54 = cube root 27 * cube root 2 = 3 cube root 2
The rule is to factor the number and look for perfect squares or cubes, etc.
If a logarithm has a coefficient, then the coefficient can also be written as the exponent of the input of the logarithm. In other words, if you have the logarithm alog(x), that is equal to log(x^a). So the expression can be rewritten:
log(x^2)+log(y^3)
If tow logarithms of the same bases are added together that is equal to the logarithm of the product of the inputs of the two original logarithms. In other words, given log(x)+log(y), it can also be written as log(xy). So the expression can be combined into one logarithm:
log(x^2 * y^3)
The number 4,770,000 in appropriate scientific notation would be 4.770000x10^16
Answer:
4,600
Step-by-step explanation:
To solve this problem, we need to multiply add 15% of 4,000 back to 4,000.
First, change 15% into a decimal:
15% -> 
-> 0.15
Next, multiply 4,000 by 0.15:
The last step is to add the 600 back to 4,000:
The population of Smallburg the following year was 4,600.
Given:
USD: 104.51
Mexican pesos: 1,322.14
1,322.14 / 104.51 = 12.65
1 US Dollar is equal to 12.65 Mexican Pesos
or
104.51 / 1,322.14 = 0.079
1 Mexican peso is equal to 0.079 US Dollars.
