Question

This problem:
(4x^5 y^2/ -2 x^3 y^2) sense this is divided I would subtract the exponents but sense it has parentheses i add them ? Im confused if the answer is -2 x^2 y or 4 x^8 y^4 if its neither then what am I doing wrong also the whole problem is the the exponent of 2

Answer 1

It looks like
\[ \left(\frac{4x^5y^2}{-2x^3y^2}\right) \]
?

Answer 2

yes and out side the parenthese a ^2

Answer 3

oh okay

\[ \left(\frac{4x^5y^2}{-2x^3y^2}\right)^2 \]
We can simplify inside the parentheses first to make it easier
\[ \begin{split}
\left(\frac{4}{-2} \frac{x^5}{x^3} \frac{y^2}{y^2}\right)^2 &= \left(-2\frac{\cancel{x*x*x}*x*x}{\cancel{x*x*x}} \cancel{\frac{y^2}{y^2}}\right)^2\\
&= \left(-2x^2\right)^2
\end{split}\]

Then the properties we use to simplify are called "power to a power" and "product property"
(ab)^k = a^k b^k
(a^k)^h = a^(kh)

Answer 4

okay thank you and its still subtraction sense y=0 i leave it out answer -2 x2 ?

Answer 5

uhh yeah, we still subtract the exponents to simplify inside the parentheses
the parentheses don't really affect the actual process, they're just there to tell us that everything in the parentheses is being squared

that's not quite the answer, since the entire thing is still being squared, so we essentially distribute the exponent "2" to each factor

Answer 6

does that make sense?