Simplify.
(xz^3) (x^2 y^-1)^-3
__________
2z^2
using only positive exponents how do I simplify this?
use the / symbol for division or to show fractions, so ...
(xz^3) (x^2 y^-1)^-3 / (2z^2) , those brackets are needed, or else we would divide by only 2
= (x z^3)(x^-3 y^3) / (2z^2)
= (x z^(3-3-2) y^3) / 2
= x y^3 / (2z^2)
(xz^3) (x^2 y^-1)^-3 / (2z^2)
(xz^3) (x^-6 y^3) / (2z^2)
(x^-5 y^3 z^3)/(2z^2)
(y^3 z) / (2x^5)
messed up, go with oobleck
To simplify the expression, we can start by simplifying the numerator and denominator separately.
Let's start with the numerator:
(xz^3)(x^2y^-1)^-3
First, simplify (x^2y^-1)^-3:
Recall that when raising a power to a negative exponent, you can rewrite it as the reciprocal raised to the positive exponent.
(x^2y^-1)^-3 = (1/x^2y)^3
= 1^3 / (x^2y)^3
= 1 / (x^6y^3)
Now, substitute this value back into the numerator:
xz^3 * (1 / (x^6y^3))
= xz^3 / (x^6y^3)
Moving on to the denominator:
We need to simplify 2z^2.
Now, combine the simplified numerator and denominator:
(xz^3 / (x^6y^3)) / (2z^2)
To divide fractions, we can multiply the numerator by the reciprocal of the denominator. In this case, the reciprocal of 2z^2 is 1 / (2z^2).
So, we have:
(xz^3 / (x^6y^3)) * (1 / (2z^2))
Multiplying these fractions:
(x * 1) * (z^3 * 1) / (x^6 * y^3 * 2 * z^2)
Now, let's simplify this expression further:
x * z^3 / (x^6 * y^3 * 2 * z^2)
To simplify the expression even more, we can cancel out common factors between the numerator and denominator:
First, let's cancel out z^3 and z^2, leaving us with:
x / (x^6 * y^3 * 2)
Further simplification can be done if there are any common factors or factors that can be simplified in the remaining terms. Otherwise, this is the simplified form.