Question

(3/5y^9)^3
write in simplest form

Answer 1

Hello there! Hope I can be of assistance

I assume you mean
`\left((3)/(5)y^9\right)^3`

With this in mind! Let us begin!


`\mathrm{Multiply\:fractions}: \:a\cdot (b)/(c)=(a\:\cdot \:b)/(c) \ \textgreater \ (3y^9)/(5) \ \textgreater \ \left((3y^9)/(5)\right)^3`


`\mathrm{Apply\:exponent\:rule}: \left((a)/(b)\right)^c=(a^c)/(b^c) \ \textgreater \ (\left(3y^9\right)^3)/(5^3)`


`\mathrm{Apply\:exponent\:rule}: \left(a\cdot \:b\right)^n=a^nb^n \ \textgreater \ \left(3y^9\right)^3=3^3\left(y^9\right)^3 \ \textgreater \ (3^3\left(y^9\right)^3)/(5^3)`


`\mathrm{Apply\:exponent\:rule}: \left(a^b\right)^c=a^(bc) \ \textgreater \ y^(9\cdot \:3) \ \textgreater \ Refine \ \textgreater \ y^(27) \ \textgreater \ (3^3y^(27))/(5^3)`

Simply refine it once more

`(27y^(27))/(125)`

Hope this helps!