How do you use the laws of exponents to simplify the expression $\frac{{(6 y^{3})}^{4}}{2 y^{5}}$ $(6y^3)^4/(2y^5)$ ?

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How do you use the laws of exponents to simplify the expression $\frac{{(6 y^{3})}^{4}}{2 y^{5}}$ $(6y^3)^4/(2y^5)$ ?

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Answer 1 · 2015-05-09T20:45:06

The Laws of Exponents relevant here are
1. ${(b c)}^{m} = b^{m} \cdot c^{m}$ $(bc)^m = b^m*c^m$
2. ${(b^{m})}^{n} = b^{m n}$ $(b^m)^n = b^(mn)$
3. $b^{- m} = \frac{1}{b^{m}}$ $b^(-m) = 1/(b^m)$
4. $b^{m} \cdot b^{n} = b^{m + n}$ $b^m*b^n = b^(m+n)$

$\frac{{({(6 y)}^{3})}^{4}}{2 y^{5}}$ $(((6y)^3)^4)/(2y^5)$

$= \frac{{(6 y)}^{12}}{2 y^{5}} by Rule [2]$ $= ((6y)^12)/(2y^5) " by Rule [2]"$

$= \frac{6^{12} \cdot y^{12}}{2 y^{5}} by Rule [1]$ $= (6^12*y^12)/(2y^5) " by Rule [1]"$

$= \frac{6^{12}}{2} \cdot y^{12} \cdot y^{- 5} by Rule [3]$ $=6^12/2 * y^12*y^(-5) " by Rule [3]"$

$= \frac{6^{12}}{2} y^{7} by Rule [4]$ $= 6^12/2y^7 " by Rule [4]"$

You could evaluate $\frac{6^{12}}{2}$ $6^12/2$ but that's just arithmetic.

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How do you use the laws of exponents to simplify the expression $\frac{{(6 y^{3})}^{4}}{2 y^{5}}$ $(6y^3)^4/(2y^5)$ ?

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How do you use the laws of exponents to simplify the expression $\frac{{(6 y^{3})}^{4}}{2 y^{5}}$ $(6y^3)^4/(2y^5)$ ?