How do you simplify #((1/2)x^4)^3#?

1 Answer
Tony B
May 26, 2016

# (x^12)/8#

Explanation:

This is the same as #(x^4)^3xx(1/2)^3#

#(x^(4xx3))xx1/(2^3)#

#x^12xx1/8 " "->" " (x^12)/8#

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Further explanation:

Consider:#" "(x^4)^3# This is another way of writing #x^4xxx^4xxx^4#

Think for a moment about #axxa -> a^1xxa^1=a^(1+1) = a^(2xx1)=a^2#

so #x^4xxx^4xxx^4= x^(4+4+4) = x^(3xx4)#

So #(x^4)^3=x^(4xx3) = x^(12)#
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