Question

Use properties of exponents to simplify
\[\left( 27m^\frac{3}{2}n^{-6} \right)^\frac{2}{3}\]

Answer 1

yeah it typed correct this time

Answer 2

one at at time
\[27^{\frac{2}{3}}=\sqrt[3]{27}^2=3^2=9\]

Answer 3

\[(m^{\frac{3}{2}})^{\frac{2}{3}}=m^{\frac{3}{2}\times \frac{2}{3}}=m^1=m\]\]

Answer 4

thye cancel each other out correct

Answer 5

they even

Answer 6

use the power of a power law

\[(x^a)^b= x^{a \times b}\]

so its

\[(3^3)^{\frac{2}{3}}\times (m^{\frac{3}{2}})^{\frac{2}{3}} \times (n^{-6})^{\frac{2}{3}}\]

Answer 7

\[(n^{-6})^{\frac{2}{3}}=n^{-6\times \frac{2}{3}}=n^{-4}=\frac{1}{n^4}\]

Answer 8

yes they cancel

Answer 9

ok i think i already asked this question, i ment to type something different, i am so sorry, do you want me to close this and ask agian?