# How do you simplify  (y^6)^-3 * y^12?

May 13, 2015

After simplifying you get ${y}^{-} 6$ or $\frac{1}{{y}^{6}}$
To calculate this you use these properties of powers:

1) ${\left({a}^{m}\right)}^{n} = {a}^{m \cdot n}$
and
2) ${a}^{m} \cdot {a}^{n} = {a}^{m + n}$
and
3) ${a}^{-} m = \frac{1}{a} ^ m$
After using 1) for the first part you get ${y}^{-} 18 \cdot {y}^{12}$
Then after using 2) you get ${y}^{-} 6$
Finally to get rid of the negative exponent you can use 3) to get the fraction.
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