How do you simplify ${(6 x^{4} y^{8})}^{3}$ $(6x^4y^8)^3$ ?

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How do you simplify ${(6 x^{4} y^{8})}^{3}$ $(6x^4y^8)^3$ ?

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Answer 1 · 2016-02-29T17:32:07

$216 x^{12} y^{24}$ $216 x^12 y^24$

Explanation:

${(6 x^{4} y^{8})}^{3}$ $(6x^4y^8)^3$

Applying exponential rule, ${(a \cdot b)}^{n} = a^{n} b^{n}$ $(a\cdot b)^n=a^nb^n$

$= 6^{3} {(x^{4})}^{3} {(y^{8})}^{3}$ $=6^3(x^4)^3(y^8)^3$

$($ $($ ${(x^{4})}^{3} = x^{12} and {(x^{8})}^{3} = x^{24}$ $(x^4)^3=x^12 and (x^8)^3 =x^24$ by applying exponent rule: ${(a^{b})}^{c} = a^{b \cdot c}$ $(a^b)^c=a^{b\cdot \c}$ $)$ $)$

$= 6^{3} x^{12} y^{24}$ $=6^3x^{12}y^{24}$

( $6^{3} = 216$ $6^3=216$ )

$= 216 x^{12} y^{24}$ $=216x^{12}y^{24}$

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How do you simplify ${(6 x^{4} y^{8})}^{3}$ $(6x^4y^8)^3$ ?

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