express the compound fraction in lowest terms:[15p^3q/3mn^2/[5p^5q^3/6n^3.
I know 6 is right but the exponents have me confused?
To express the compound fraction in lowest terms, we need to simplify both the numerator and the denominator separately, and then divide the simplified numerator by the simplified denominator.
Let's start by simplifying the numerator:
Numerator: 15p^3q
The numerator is already in its simplest form.
Now, let's simplify the denominator:
Denominator: 3mn^2/[5p^5q^3/6n^3]
To simplify the denominator, we need to divide by the fraction in the denominator.
To divide by a fraction, we multiply by its reciprocal (flipped version).
Reciprocal of [5p^5q^3/6n^3] is [6n^3/5p^5q^3].
So, the denominator becomes: 3mn^2 * [6n^3/5p^5q^3]
Now, let's simplify the denominator:
3mn^2 * [6n^3/5p^5q^3]
To multiply fractions, we multiply the numerators together and the denominators together.
Denominator = (3 * 6 * m * n^2 * n^3) / (5 * p^5 * q^3)
= (18mn^5) / (5p^5q^3)
Now, we can rewrite the compound fraction in its simplified form as:
Numerator / Denominator = (15p^3q) / [(18mn^5) / (5p^5q^3)]
Finally, to divide by a fraction, we multiply by its reciprocal (flipped version). So, we can rewrite the compound fraction in lowest terms as:
(15p^3q) * [(5p^5q^3) / (18mn^5)]
We can simplify further if required, by multiplying the numerators and denominators together.