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# How Do You Add Variables With Exponents?

The basic rule in adding and subtracting variables with exponents is they must be like terms. Like terms consist of the same variable or set of variables raised to the same power. The numerical coefficients of these terms may vary, and these are the elements that undergo the addition or subtraction process. The algebraic expressions 2x, 7x and x are like terms, as well as, 4ab^2 and 21ab^2.

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To simplify an algebraic expression, look for like terms. If two terms have the same variables but have different exponents, they cannot be combined. In the expression 8x - 10y + 3x, the like terms are 8x and 3x. The sum of their numerical coefficients must be attached to the common variable and corresponding exponent. Thus, the simplified version of the expression is 11x – 10y. The two remaining terms cannot be combined because they are not like terms.

In the example 6x^2y^2z + xyz - x^2y^2z, the like terms are 6x^2y^2z and x^2y^2z. Subtraction is the operation necessary to combine these two terms. The difference is 5x^2y^2z. Therefore, 5x^2y^2z + xyz is the given expression in its simplified form. The variables and exponents in the like terms remain unaltered in the final equation.

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## What Are the Division Properties of Exponents?

A: The division properties of exponents are: when dealing with like bases, exponents are subtracted when the bases are divided; when an entire quotient is rai... Full Answer >Filed Under: -
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## What Are the Steps in Multiplying Polynomials With Exponents?

A: The steps for multiplying polynomials with exponents vary depending on the complexity of the polynomials. If the equation has only one variable, the answer... Full Answer >Filed Under: -
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## What Is the Way to Multiply Exponents With Different Bases?

A: When multiplying exponents with different bases, multiply the bases first. For instance, when multiplying y^2 * z^2, the formula would change to (y * z)^2. Full Answer >Filed Under: -
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## What Is a Rational Exponent Notation?

A: Rational or fractional exponents are another way of notating that some root of a base number should be taken, without using a radical sign. For instance, 1... Full Answer >Filed Under: