algebraic expression with exponents questions

(-2³x^-6)(36x²)/(2(-3³x^-3)=

(-8x^-6)(36x²)/(-54x^-3)=

(-8)(36x²)(x³)/-54x⁶⁼

-288x⁵/-54x⁶=

-288/-54x=

16/3x

not totally sure. I wouldn't trust this to be right.

First you could call this "distributing" the exponent, not sure what the real name is for this step.

\(\frac{(-2x^{-2})^3(6x)^2}{2(-3x^{-1})^3}=\frac{(-2^3x^{-2*3})(6^2x^2)}{2(-3^3x^{-1*3})}=\frac{(-8x^{-6})(36x^2)}{2(-27x^{-3})}\)

Now all terms with negative exponents in the numerator go to the denominator and lose the negative sign and vice versa.

\(\frac{(-8x^3)(36x^2)}{2x^6(-27)}\)

Now multiply the things in the numerator and the things in the denominator together.

\(\frac{-288x^{3+2}}{-54x^6}=\frac{-288x^{5}}{-54x^6}\)

Now reduce the fraction by 18x⁵

\(\frac{-288x^{5}}{-54x^6}=\frac{16}{3x^{6-5}}=\frac{16}{3x}\)

Same as guest.