Pat shows that 16 1/2= the square root of 16. What is one possible way pat could have shown this correctly?
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The base 16 is the same as 4*4.
From there, the rule [tex](a*b)^c = a^c*b^c[/tex] is used to get [tex](4*4)^{1/2} = 4^{1/2}*4^{1/2}[/tex]
Afterward, the exponents are added getting 1/2+1/2 = 2/2 = 1. The rule is [tex]a^b*a^c = a^{b+c}[/tex] which only works if the bases are both the same.