How do you simplify the expression #8a^5(a^-2)^6 div (a^-1)^-3#?

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Answer 1 · 2016-04-05T21:49:17

#8/a^10#

Recall the following rules of exponents :

#x^(-n)=1/x^n#

#(x^m)^n=x^(mn)#

#x^m*x^n=x^(m+n)#

#x^m/x^n=x^(m-n)#

#a/b-:c/d=a/bxxd/c#

Now using these rules in conjunction leads to

#8a^5(a^(-12))-:a^3#

#=8/a^7xx1/a^3#

#=8/a^10#