Question

Simplify the expression x^-4y^3x^4y^2

Answer 1

y^5

Answer 2

thanks

Answer 3

lets RVW some pro[perties of exponents, but before we do this, you know that what your equation really says is:

\(\large\color{black}{ \displaystyle x^{-4} \color{red}{\times}y^3\color{red}{\times}x^4\color{red}{\times}y^2 }\) (multiplication)

And also that this can be re-written as:

\(\large\color{black}{ \displaystyle x^{-4} \color{red}{\times} x^4\color{red}{\times} y^3\color{red}{\times} y^2 }\)

Answer 4

The rules of exponents say that:

\(\large\color{black}{ \displaystyle a^b\times a^c=a^{b+c} }\)

And that,

\(\large\color{black}{ \displaystyle a^{0}=1\quad \quad \quad \color{blue}{ {\rm provided~that}~~a\ne 0}}\)

Answer 5

So you would end up getting:

\(\large\color{black}{ \displaystyle x^{-4} \color{red}{\times} x^4\color{red}{\times} y^3\color{red}{\times} y^2 }\)

\(\large\color{black}{ \displaystyle x^{-4+4}\color{red}{\times} y^{3+2}=x^0\color{red}{\times}y^5=1\color{red}{\times}y^5=y^5 }\)