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How do you find the gcf and LCM of numbers with variables and-exponents?
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.
What exactly has the same variable and exponents?
In algebra, expressions that have the same variable and exponents are considered like terms. For example, the terms (3x^2) and (5x^2) are like terms because they both contain the variable (x) raised to the same exponent of 2. Like terms can be combined through addition or subtraction, while terms with different variables or exponents cannot be combined in this way.
Can algebraic expressions have exponents?
Yes.
What is the process for evaluating expressions called?
An algebraic expression is a process for evaluating expressions. Replacing variables with numerals and following a standard order of operations is used for the process.
What is an expression that substitutes numbers for the variables in the expressions?
It is "evaluating".
How do you find GCF with variables and exponents?
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.
How do you find the gcf and LCM of numbers with variables and-exponents?
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.
Rule that states the sequence to be used when evaluating expressions?
Q: What is the rule that states the sequence to be used when evaluating expressions? A: The rule that states the sequence to be used when evaluating expressions is know as the "order of operations."
What exactly has the same variable and exponents?
In algebra, expressions that have the same variable and exponents are considered like terms. For example, the terms (3x^2) and (5x^2) are like terms because they both contain the variable (x) raised to the same exponent of 2. Like terms can be combined through addition or subtraction, while terms with different variables or exponents cannot be combined in this way.
Can algebraic expressions have exponents?
Yes.
What is a process for evaluating expressions?
Order of Operations
What is the process for evaluating expressions called?
An algebraic expression is a process for evaluating expressions. Replacing variables with numerals and following a standard order of operations is used for the process.
What is an expression that substitutes numbers for the variables in the expressions?
It is "evaluating".
When dividing variables with exponents subtract exponents?
Yes. When you divide one variable with an exponent from another, you subtract the exponents
What four-steps should be used in evaluating expressions Can these steps be skipped or rearranged?
You should do everything in the parenthesis. Then you do the exponents. Then you multiply and divide from left to right. Then finish with addition and subtraction doing left to right. You cannot do these out of order.
Can you add unknowns that have coefficients and exponents?
the unknowns must be the same variable and the exponents have to be the same. examples) x4 + y4 cannot be added because they are not the same variable. x3 + x2 cannot be added because they have different exponents. 3y6 + 5y6 can be added because they have the same variable and exponents. (answer: 8y6)
What is the definition of equivalen variable expressions?
Two expressions are "equivalent" if they have the same result for any values of the variable or variables.
