# Can you add powers with different bases?

## Can you add powers with different bases?

It is possible to multiply exponents with different bases, but there’s one important catch: the exponents have to be the same. First, multiply the bases together. Then, add the exponent. Instead of adding the two exponents together, keep it the same.

## How do you add powers with different powers?

To add or subtract with powers, both the variables and the exponents of the variables must be the same. You perform the required operations on the coefficients, leaving the variable and exponent as they are.

Do you add a power to a power?

When raising a power to a power in an exponential expression, you find the new power by multiplying the two powers together. For example, in the following expression, x to the power of 3 is being raised to the power of 6, and so you would multiply 3 and 6 to find the new power.

### Can you add indices?

When expressions with the same base are multiplied, the indices are added. You could verify this by evaluating both sides separately. When expressions with the same base are divided, the indices are subtracted.

### Can you add 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.

How do you combine exponents?

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.

#### When bases are same and powers are different?

When the bases and powers are different. Consider two exponents with different bases and powers an and bm. Here, the bases are a and b. The powers are n and m. When the exponents with different bases and different powers are multiplied, each exponent is evaluated separately and then multiplied.

Can you add and subtract with the same powers?

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. Because the variables are the same ( x) and the powers are the same (there are no exponents, so the exponents must be 1), you can add the variables.

## Do you multiply with power or keep the base the same?

Bases – raise it with power to another – multiply the exponents and keep the base same. Bases – dividing the like ones – ‘Numerator Exponent – Denominator Exponent’ and keep the base same. (Division Law)

## When do you combine powers of the same base?

Caution! The rule above works only when multiplying powers of the same base. For instance, (x3)(y4) = (x)(x)(x)(y)(y)(y)(y) If you write out the powers, you see there’s no way you can combine them. Except in one case: If the bases are different but the exponents are the same, then you can combine them.

When do you add exponents when the bases are the same?

In other words, when the bases are the same, you find the new power by just adding the exponents: Caution! The rule above works only when multiplying powers of the same base. For instance, If you write out the powers, you see there’s no way you can combine them.

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