Question

How do you multiply and simplify `\frac { 7x y ^ { 4} } { 9z ^ { 2} } \cdot \frac { 45z ^ { 6} } { 21x ^ { 4} y }`?

Answer 1

`(5y^(3)z^(4))/(3x^3)`

Explanation:

Step 1. Place all terms into a single fraction

`(7xy^4 45z^6)/(9z^2 21x^4y)`

Step 2. Multiply integers and simplify. Rearrange variables so they are in the same order.
`(5xy^4z^6)/(3x^4 y z^2)`

Step 3. Subtract exponents of like variables (top minus bottom). Put them all in the numerator.
`(5x^(1-4)y^(4-1)z^(6-2))/(3)`
`(5x^(-3)y^(3)z^(4))/(3)`

Step 4. Positive exponents will remain in the numerator. Negative exponents will go to the denominator and be made positive.
`(5y^(3)z^(4))/(3x^3)`