How do you multiply #(5x^2)/(3y) * (9xy)/20 *( 4y^2)/(3x^2)#?

Question

Eva Adamson · Accepted Answer

The answer is #xy^2#.

#(5x^2)/(3y) * (9xy)/(20) *(4y^2)/(3x^2)# Multiply the numerators and denominators. #(5x^2*9xy*4y^2)/(3y*20*3x^2)=# #(180x^3y^3)/(180x^2y)# Simplify. #(cancel(180)x^3y^3)/(cancel(180)x^2y)=# #(x^3y^3)/(x^2y)# Apply the exponent rule #a^m/a^n=a^(m-n)# #x^(3-2)y^(3-1)=# #xy^2#

Ethan Adkins · Answer

undefined To multiply the given expressions, you can follow these steps:

1. Multiply the numerators together: (5x^2) * (9xy) * (4y^2)
2. Multiply the denominators together: (3y) * (20) * (3x^2)
3. Simplify each term in the numerator and denominator:
   - In the numerator, multiply the coefficients: 5 * 9 * 4 = 180
   - Multiply the variables with the same base by adding their exponents: x^2 * x * y * y^2 = x^(2+1) * y^(1+2) = x^3 * y^3
   - In the denominator, multiply the coefficients: 3 * 20 * 3 = 180
   - Multiply the variables with the same base by adding their exponents: y * x^2 = y^1 * x^2
4. Write the simplified expression: (180x^3y^3) / (180yx^2)
5. Cancel out any common factors between the numerator and denominator:
   - Divide both the numerator and denominator by 180: (180x^3y^3) / (180yx^2) = (x^3y^3) / (yx^2)
   - Divide y^3 by y: (x^3y^3) / (yx^2) = (x^3y^2) / (x^2)
6. Simplify the expression further by subtracting the exponents: (x^3y^2) / (x^2) = x^(3-2) * y^2 = xy^2

Therefore, the simplified expression is xy^2.