When do i subtract exponents

Alright so in order for us to simplify this we have to look for two things. One, are our bases or variables the same; and two, are our exponents the same?

Both things have to be true in order for us to add these two terms together. This same process of adding and subtracting with exponents is also called combining like terms, which may sound more familiar to you. Well, they are the same thing. Okay, so looking back at our problem we can see that our bases are the same, and our exponents are the same.

This means we have two like terms that can be combined together. So, to actually combine them here is what you do:. In this problem our coefficients are 5 and 9. Copyright Notice. Jonathan Certified Tutor. Kenneth Certified Tutor. Irene Certified Tutor. University of Patras, Bachelor of Science, Mathematics. Report an issue with this question If you've found an issue with this question, please let us know.

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Your Full Name. Phone Number. Zip Code. For example:. Multiplying exponents depends on a simple rule: just add the exponents together to complete the multiplication. If the exponents are above the same base, use the rule as follows:. When you have an exponent raised to another exponent, multiply the two exponents together to find the result, according to:. Use the basic rules for exponents to simplify any complicated expressions involving exponents raised to the same base.

If there are different bases in the expression, you can use the rules above on matching pairs of bases and simplify as much as possible on that basis. You'll require a few of the rules listed above. First, use the rule for exponents raised to powers to make it:. Multiplying a number by another number with the same base is equivalent to multiplying their coefficients and adding their exponents. Therefore, if we want to add two quantities written in scientific notation whose exponents do not match, we can simply write one of the powers of 10 as the product of two smaller powers of 10 , one of which agrees with the other term.

Alternately, if we want to preserve the exponent of the term with the larger power of 10 , we can simultaneously multiply and divide the other term by a power of 10 , applying the rule for multiplication of exponents in one case and dividing the coefficient in the other.

It is this procedure that we outline below. Here are the steps to adding or subtracting numbers in scientific notation : Determine the number by which to increase the smaller exponent by so it is equal to the larger exponent.