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Question
State the product law of exponents.
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Solution
State the product law of exponents.
If a is any real number and m,n are positive integers, then
`a^m xx a^n = a^(m+n)`
By definition, we have
`a^m xx a^n = (a xx a xx ...m " factor") xx (a xx a xx ...n "factor")`
`a^m xx a^n = a xx a xx..... "to " (m+n)` factors
`a^m xx a^n = a^(m+n)`
Thus the exponent "product rule" tells us that, when multiplying two powers that have the same base, we can add the exponents.
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