How do you evaluate the expression #(2^3)^2/(2^-4# using the properties?

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Answer 1 · 2017-04-08T06:19:08

#2^10 =1024#

To begin simplifying, we apply two of the laws of indices.

#color(red)((x^m)^n = x^(mxxn))" "and " " color(blue)(1/x^-m = x^m)#

#(color(red)((2^3)^2))/color(blue)(2^-4) = color(red)(2^6)xxcolor(blue)(2^4)#

Now apply the multiply law of indices (add the indices of like bases)

#2^m xx2^n = 2^(m+n)#

#2^6 xx 2^4 = 2^10#

"Evaluate means to find the value of the expression, so we must give a number answer."

#2^10 = 2xx2xx2xx2xx2xx2xx2xx2xx2xx2 = 1024#