Question

# How do you simplify (\frac { 24x ^ { 5} y ^ { 4} } { 3x ^ { - 2} y } )?

How do you simplify (\frac { 24x ^ { 5} y ^ { 4} } { 3x ^ { - 2} y } )?

Answer 1

$8 {x}^{7} {y}^{3}$

#### Explanation:

$\left(\setminus \frac{24 {x}^{5} {y}^{4}}{3 {x}^{- 2} y}\right)$

Remember a fraction is a division.
When you are dividing exponents you subtract them.
Also, remember you can only subtract exponents that are over the same variable.

$\left(\setminus \frac{24 \textcolor{red}{{x}^{5}} \textcolor{g r e e n}{{y}^{4}}}{3 \textcolor{red}{{x}^{- 2}} \textcolor{g r e e n}{y}}\right)$

So... our subtractions here are

color(red)(x^(5-(-2))=color(red)(x^(5+2))=color(red)(x^7)

color(green)(y^(4-1) $< - - -$ Remember if there is no exponent over the variable it is a $1$
color(green)(y^(4-1)=color(green)(y^3)

Now move your subtracted exponents to wherever the LARGER exponent was. In this case $x$ and $y$ both had the larger exponent in the numerator.

$\left(\setminus \frac{24 \textcolor{red}{{x}^{7}} \textcolor{g r e e n}{{y}^{3}}}{3}\right)$

Now make sure you check if the numbers are divisible.
They are...
Let's go ahead and divide them.

$\left(\setminus \frac{24 \textcolor{red}{{x}^{7}} \textcolor{g r e e n}{{y}^{3}}}{3}\right)$

$\frac{24}{3} = 8$

So...

$8 \textcolor{red}{{x}^{7}} \textcolor{g r e e n}{{y}^{3}}$

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