Question

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

Answer 1

Answer:

$\frac{2p^3}{m^4}$

Step-by-step explanation:

Four of the exponent rules applied are

1. $x^0 = 1$
2. $x^1 = x$
3. $x^mx^n = x^{m+n}$
4. $\frac{x^m}{x^n} = x^{m-n}$
5. $x^{-m} = \frac{1}{x^m}$

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

$\frac{4p^4m^{-2}}{2p^1m^2}$

$\frac{p^4}{p^1} = p^{4-1} = p^3$   by rule 4

$\frac{m^{-2}}{m^2} = m^{-2-2} = m^{-4}$

So the entire expression becomes

$2p^3m^{-4}$

$m^{-4} = \frac{1}{m^4}$   using rule 5

Expression simplifies to

$\frac{2p^3}{m^4}$