Question 253671
Note: instead of typing "square root2", type "sqrt(2)" and surround it with curly braces to get {{{sqrt(2)}}}


Remember that {{{(a^b)/(a^c)=a^(b-c)}}}. In other words, if you divide exponential expressions (with the same base), you just subtract the exponents.





{{{(7^(3*sqrt(2)))^""/(7^(sqrt(2)))^""}}} Start with the given expression.



{{{7^(3*sqrt(2)-sqrt(2))^""}}} Use the identity {{{(a^b)/(a^c)=a^(b-c)}}} 



{{{7^(sqrt(2)(3-1))^""}}} Factor out the GCF {{{sqrt(2)}}} from the exponent.



{{{7^(sqrt(2)(2))^""}}} Combine like terms.



{{{7^(2*sqrt(2))^""}}} Rearrange the terms.




So {{{(7^(3*sqrt(2)))^""/(7^(sqrt(2)))^""=7^(2*sqrt(2))^""}}}