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avatar+386 

Would it be ok to combine both of the following laws:

 

(a/b)^m = a^m/b^m

 

(a^m)^n = a^m(n)

 

Such as in this case:

 

(a/b)^ m(n)

 

= (a^m/b^m)^n

 

 

Thanks!

 Aug 3, 2016

Best Answer 

 #3
avatar+9665 
+5

\(\left(\dfrac{a}{b}\right)^{m\cdot n}\)

\(=\left(\dfrac{a^m}{b^m}\right)^n\)

This is correct, this also equals

\(\dfrac{a^{mn}}{b^{mn}}\)

 Aug 3, 2016
 #1
avatar
+5

(a/b)^m = a^m/b^m - TRUE if a, b and m are positive.

 

(a^m)^n = a^m(n) - TRUE if a, m and n are positive.

 

(a/b)^ m(n) =(a^m/b^m)^n - TRUE if a, b, m and n are positive.

 Aug 3, 2016
 #3
avatar+9665 
+5
Best Answer

\(\left(\dfrac{a}{b}\right)^{m\cdot n}\)

\(=\left(\dfrac{a^m}{b^m}\right)^n\)

This is correct, this also equals

\(\dfrac{a^{mn}}{b^{mn}}\)

MaxWong Aug 3, 2016

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