-10m^-1y^0r
_______________
-14m^-7y^-3r^-4
Please help me simplify this polynomial.
(10/14) m^6 y^3 r^5
but 10/14 = 5/7
To simplify this polynomial expression, we can use the rules of exponents.
First, let's simplify the variables. We can combine the m terms by subtracting their exponents:
m^(-1) / m^(-7) = m^(-1 - (-7)) = m^6
Similarly, we can simplify the y terms:
y^0 / y^(-3) = y^(0 - (-3)) = y^3
Finally, let's simplify the r terms:
r^(-1) / r^(-4) = r^(-1 - (-4)) = r^3
Now, let's put everything together:
(-10m^-1y^0r) / (-14m^-7y^-3r^-4) = (-10 / -14) * (m^6 / m^-7) * (y^3 / y^-3) * (r^3 / r^-4)
Dividing -10 by -14 gives us 5/7, so we have:
(5/7) * (m^6 / m^-7) * (y^3 / y^-3) * (r^3 / r^-4)
In the numerator, m^6 / m^-7 can be simplified by subtracting their exponents:
m^(6 - (-7)) = m^13
Similarly, in the denominator, y^3 / y^-3 simplifies to:
y^(3 - (-3)) = y^6
And the r terms simplify to:
r^(3 - (-4)) = r^7
Now, what we have left is:
(5/7) * m^13 * y^6 * r^7
This is the simplified form of the given polynomial expression.