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what is the power rule for exponents. Take a moment to contrast how this is different from the product rule for exponents found on the previous page. In a similar way to the product rule we can simplify an expression such as latexfracymynlatex where latexmnlatex.
But first lets look at expanding Power of Power without using this rule. 103 10 times 10 times 10 1000 103 10 10 10 1000. Expanding Power of Power The Long Way.
What we actually want to do is use the power rule for exponents.
A x y a x y axyax cdot y a x y a x y In words the above expression basically states that for any value to an exponent which is then all raised to another exponent you can simply combine the exponents into one by just multiplying them. 8 2 could be called 8 to the power 2 or 8 to the second power or simply 8 squared. Power Rule of Exponents amn amn When raising an exponential expression to a new power multiply the exponents. 4x5 2x3 3x2 5.