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To add exponents, both the exponents and variables should be alike. You add the coefficients of the variables leaving the exponents unchanged. Only terms that have same variables and powers are added. This rule agrees with the multiplication and division of exponents as well.

## What happens when you add two variables with exponents?

To add or subtract with powers, both the variables and the exponents of the variables must be the same. When adding or subtracting with powers, the terms that combine always have exactly the same variables with exactly the same powers. These rules are true for multiplying and dividing exponents as well.

Can you add same variables with different exponents?

In order to add or subtract variables with exponents, you need to have like bases and like exponents, which means that the bases and exponents are the same. Even though the exponents are the same, these cannot be added or subtracted because their bases or exponents are different.

What is the rule when adding variables?

Whether you add or subtract variables, you follow the same rule, even though they have different operations: when adding or subtracting terms that have exactly the same variables, you either add or subtract the coefficients, and let the result stand with the variable. For example: Addition.

### How do you add and multiply exponents?

You can only multiply terms with exponents when the bases are the same. Multiply the terms by adding the exponents. For example, 2^3 * 2^4 = 2^(3+4) = 2^7. The general rule is x^a * x^b = x^(a+b).

### How do you add exponents with different bases and powers?

To multiply terms with the same base, keep the same base and add the powers together. To multiply terms with different bases but the same power, raise the product of the bases to the power. This can be expressed as: If the exponents have coefficients attached to their bases, multiply the coefficients together.

Can you add powers with the same base?

When terms have the same base and exponent they can be added or subtracted. Answer: Terms that have the same base and exponent can be added or subtracted. These are often referred to as “like terms”.

What are the rules when adding exponents?

The first rule to remember when adding with exponents is the order of operations: parenthesis, exponents, multiplication, division, addition, subtraction. This order of operations places exponents second in the solving scheme. So if you know both the base and the exponent, solve them before moving on.

#### How do you add numbers with different exponents?

Adding Numbers With Exponents By Hand Solve the first exponential expression. An exponential expression has a base (large number) and exponent (small number). Solve the second exponential expression. To do this, multiply the base by itself the number of times indicated by the exponent. Add the two values together.

#### When to add or subtract exponents?

When we multiply two numbers with exponents, we add exponents only when they have common base. Similarly, when we divide two numbers with exponents, we should subtract the exponent of denominator from that of numerator provided they have common base.

Are variables with different exponents considered like terms?

Like terms : The terms having the same literal (variable) with same exponents are called Like terms. Example: 1) 12x and -5x 2) 4x 2 and ½ x 2 Unlike terms : The terms having the same variable with different exponents or different variable with same exponents are called Unlike terms .