For the greatest common factor, you check which variables appear in each of the expressions. In the case of exponents, you take the lowest exponent for each variable. For the least common multiple, you take each variable, whether it appears in all of the expressions involved, or only in some of them. In the case of the exponents, you take the greatest exponent for each variable. If there are numeric coefficients (numbers as products), you take either the gcf or the lcm of those in the usual way.
2^2 = 4
75 = 3 x 52
2 x 72 = 98
22 x 32 = 36
Yes, coefficients can be fractions in algebraic expressions. Fractions may appear when coefficients are expressed in a ratio or when simplifying expressions that involve division.
For the greatest common factor, you check which variables appear in each of the expressions. In the case of exponents, you take the lowest exponent for each variable. For the least common multiple, you take each variable, whether it appears in all of the expressions involved, or only in some of them. In the case of the exponents, you take the greatest exponent for each variable. If there are numeric coefficients (numbers as products), you take either the gcf or the lcm of those in the usual way.
For each variable, find the smallest exponent in all the expressions. If the variable does not appear in one of the expressions, it's exponent may be taken as 0. Also, remember that if a variable seems to be without an exponent, its exponent is actually 1 (that is x is the same as x1). For example, GCF(a3bc, a2c3, a3b2c3) = a2c. Exponents of a are 3, 2 and 3: smallest = 2 Exponents of b are 1, 0 and 2: smallest = 0 Exponents of c are 1, 3 and 3: smallest = 1 The same rules apply for fractional exponents.
No, order can't spontaneously appear in a macroscopic closed system which has reached thermal equilibrium.
The numbers that appear in front of the chemical formulas in a balanced equation are called coefficients. Coefficients are used to balance the equation by ensuring that the number of each type of atom is the same on both sides of the equation.
No
3 x 137 = 411
2^2 = 4
22*72 = 196
245 = 51 x 72
441 = 32 x 72
35 x 7 = 1701