Question

How do you multiply `3m ^ { - 1} n ^ { 4} \cdot m ^ { - 2} n ^ { 3}`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`3(m^-1 * m^-2)(n^4 * n^3)`

Next, use this rule for exponents to multiply the `m` and `n` terms:

`x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))`

`3(m^color(red)(-1) * m^color(blue)(-2))(n^color(red)(4) * n^color(blue)(3)) => 3m^(color(red)(-1) + color(blue)(-2))n^(color(red)(4) + color(blue)(3)) =>`

`3m^-3n^7`

We can now use this rule of exponents to eliminate the negative exponent:

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

`3m^color(red)(-3)n^7 => (3n^7)/m^color(red)(- -3) =>`

`(3n^7)/m^color(red)(3)`