How do you evaluate #5^ { 4} \cdot ( 5^ { - 3} ) ^ { 2}#?

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Answer 1 · 2017-02-03T06:04:29

#1/25#

We can use the rule that #(x^a)^b=x^(ab)# to work on the right side term:

#5^4 xx (5^-3)^2= 5^4 xx 5^(-3xx2)=5^4xx5^-6#

We can then use the rule #x^a xx x^b=x^(a+b)# to evaluate the statement:

#5^4xx5^-6=5^(4-6)=5^-2#

We can then use the rule that #x^-1=1/x# to see that:

#5^-2=(5^2)^-1=1/5^2#

And lastly, we can evaluate it:

#1/5^2=1/25#