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When can I add exponents?

Answer 1

Noah Archer

#x^a xx x^b=x^(a+b)#

Exponents can be added when two of the same base are multiplied. That is, #x^a xx x^b = x^(a+b)#. For example:

#2^3xx2^5 = 2^(3+5)=2^8#

#5^(-1)xx5^1 = 5^(-1+1) = 5^0 = 1#

#7^(1/4)xx7^(3/4) = 7^(1/4+3/4) = 7^(1)=7#

Note that this does not apply when the bases are different.

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Answer 2

Luna Angel

You can add exponents when the bases of the exponents are the same. Simply add the numerical coefficients of the terms and keep the base unchanged. For example, (2^3 + 2^4 = 2^3 \times (1 + 2) = 2^3 \times 3 = 24).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.