When can I add exponents?

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

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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