Question

How would u answer this question regarding the rules of exponents.

Answer 1

`(2p^3)/(m^4)`

Explanation:

Four of the exponent rules applied are

1. 
   `x^0 = 1`
2. 
   `x^1 = x`
3. 
   `x^mx^n = x^(m+n)`
4. 
   `(x^m)/(x^n) = x^(m-n)`
5. 
   `x^(-m) = (1)/(x^m)`

where x is any variable and m and n are constants

Let's look at the numerator

Expanding the parentheses and bringing together the like variables we get

`2pm^(-1)q^02p^3m^(-1) = 4 (p p^3) (m^(-1)m^(-1))q^0`

`pp^3 = p^1p^3 = p^(1+3)=p^4` by rules 2 and 3

`q^0 =1` by rule 1

`m^(-1)m^(-1) = m^(-1-1) = m^(-2)` Rule 3

Therefore numerator simplifies to

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

The expression becomes

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

`(p^4)/(p^1) = p^(4-1) = p^3` by rule 4

`(m^(-2))/(m^2) = m^(-2-2) = m^(-4)`

So the entire expression becomes

`2p^3m^(-4)`

`m^(-4) = (1)/(m^4)` using rule 5

Expression simplifies to

`(2p^3)/(m^4)`