How do you simplify ${((\frac{1}{2}) x^{4})}^{3}$ $((1/2)x^4)^3$ ?

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Answer 1 · 2016-05-26T16:29:59

$\frac{x^{12}}{8}$ $(x^12)/8$

This is the same as ${(x^{4})}^{3} \times {(\frac{1}{2})}^{3}$ $(x^4)^3xx(1/2)^3$

$(x^{4 \times 3}) \times \frac{1}{2^{3}}$ $(x^(4xx3))xx1/(2^3)$

$x^{12} \times \frac{1}{8} \to \frac{x^{12}}{8}$ $x^12xx1/8 " "->" " (x^12)/8$

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Further explanation:

Consider: ${(x^{4})}^{3}$ $" "(x^4)^3$ This is another way of writing $x^{4} \times x^{4} \times x^{4}$ $x^4xxx^4xxx^4$

Think for a moment about $a \times a \to a^{1} \times a^{1} = a^{1 + 1} = a^{2 \times 1} = a^{2}$ $axxa -> a^1xxa^1=a^(1+1) = a^(2xx1)=a^2$

so $x^{4} \times x^{4} \times x^{4} = x^{4 + 4 + 4} = x^{3 \times 4}$ $x^4xxx^4xxx^4= x^(4+4+4) = x^(3xx4)$

So ${(x^{4})}^{3} = x^{4 \times 3} = x^{12}$ $(x^4)^3=x^(4xx3) = x^(12)$
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