Question

How do you simplify `\frac{-m^{-2}n^{-4}}{(2m^{-2}n^{4}p^{-3})^{0}\cdot 2m^{2}n^{-4}p^{-1}}`?

Answer 1

see a solution process below:

Explanation:

First, use this rule of exponents to simplify the denominator of the fraction:

`a^color(red)(0) = 1`

`(-m^-2n^-4)/((2m^-2n^4p^-3)^color(red)(0) * 2m^2n^-4p^-1) =>`

`(-m^-2n^-4)/(1 * 2m^2n^-4p^-1) =>`

`(-m^-2n^-4)/(2m^2n^-4p^-1)`

Next, rewrite the expression as:

`(-1m^-2n^-4)/(2m^2n^-4p^-1) =>`

`-1/2(m^-2/m^2)(n^-4/n^-4)(1/p^-1) =>`

`-1/2(m^-2/m^2)(color(red)(cancel(color(black)(n^-4)))/color(red)(cancel(color(black)(n^-4))))(1/p^-1) =>`

`-1/2(m^-2/m^2) * 1 * (1/p^-1) =>`

`-1/2(m^-2/m^2)(1/p^-1)`

Next, use this rule for exponents to simplify the `m` terms:

`x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))`

`-1/2(m^color(red)(-2)/m^color(blue)(2))(1/p^-1) =>`

`-1/2(1/m^(color(blue)(2)-color(red)(-2)))(1/p^-1) =>`

`-1/2(1/m^(color(blue)(2)+color(red)(2)))(1/p^-1) =>`

`-1/2(1/m^4)(1/p^-1) =>`

`-1/(2m^4)(1/p^-1)`

Now, use these rules for exponents to simplify the `p` term:

`1/x^color(red)(a) = x^color(red)(-a)` and `a^color(red)(1) = a`

`-1/(2m^4)(1/p^color(red)(-1)) =>`

`-1/(2m^4)(p^color(red)(- -1)) =>`

`-1/(2m^4)(p^color(red)(1)) =>`

`-1/(2m^4)(p) =>`

`-p/(2m^4)`