Question

How do you simplify `((2p m^-1q^0)^-4*2m^-1p^3)/(2pq^2)` and write it using only positive exponents?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`((2 * 2)/2)((p * p^3)/p)(m^-1 * m^-1)(q^0/q^2)`

Next, cancel common terms in the numerator and denominator:

`((color(red)(cancel(color(black)(2))) * 2)/color(red)(cancel(color(black)(2))))((color(blue)(cancel(color(black)(p))) * p^3)/color(blue)(cancel(color(black)(p))))(m^-1 * m^-1)(q^0/q^2) =>`

`2p^3(m^-1 * m^-1)(q^0/q^2)`

Next, use this rule of exponents to simplify the `q` term:

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

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

`2p^3(m^-1 * m^-1)(1/q^2) =>`

`(2p^3)/(q^2)(m^-1 * m^-1)`

Now, use these rules of exponents to simplify the `m` terms:

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

`(2p^3)/(q^2)(m^color(red)(-1) * m^color(blue)(-1)) =>`

`(2p^3)/(q^2)m^(color(red)(-1)+color(blue)(-1)) =>`

`(2p^3)/(q^2)m^(color(red)(-2) =>`

`(2p^3)/(q^2)(1/m^(color(red)(- -2) =>`

`(2p^3)/(q^2)(1/m^2) =>`

`(2p^3)/(q^2m^2)`