Question

How do you simplify `zr \cdot 2z ^ { - 4} r ^ { - 3}`?

Answer 1

`2/(z^3r^2)`

Explanation:

Add exponents when multiplying:
`2z^(-3)r^(-2)=`

`2/(z^3r^2)`

Answer 2

`zr*2z^(-4)r^(-3)=2/(z^3r^2)`

Explanation:

Simplify:

`zr*2z^(-4)r^(-3)`

Take out the constant `2`.

`2zrz^(-4)r^(-3)`

Apply product rule: `a^ma^n=a^(m+n)`

`2z^(1+(-4))r^(1+(-3))`

Simplify.

`2z^(-3)r^(-2)`

Apply negative exponent rule: `a^(-m)=1/a^m`

`2/(z^3r^2)`

Answer 3

`2/(z^3r^2)`

Explanation:

We can rewrite this with the constant out front as

`2z*z^(-4)*r*r^(-3)`

When we multiply exponents, we add the powers. We now have

`2z^(-3)r^(-2)`

We can make the negative exponents positive by bringing them to the denominator. We get

`2/(z^3r^2)`

Hope this helps!