8x^7 over 9 Times 27y^2 Over 16x^3
To simplify the expression (8x^7/9) * (27y^2/16x^3), we can follow these steps:
Step 1: Simplify each fraction separately:
- For the first fraction, 8x^7/9, there isn't much simplification that can be done.
- For the second fraction, 27y^2/16x^3, we can simplify by canceling out common factors:
- Divide both the numerator and denominator by 3: (27/3)y^2/[(16/3)x^3]
- Simplify further by dividing both the numerator and denominator by 3 again: 9y^2/[(16/9)x^3]
Step 2: Combine the two fractions by multiplying them together:
- Multiply the numerators: 8x^7 * 9y^2
- Multiply the denominators: 9 * (16/9)x^3
- Simplifying, we get (8x^7 * 9y^2) / (9 * (16/9) * x^3)
Step 3: Simplify further:
- Cancel out common factors: (8/1 * 1/1) * (x^7/1 * y^2/x^3) / (1 * (16/9))
- (8 * 1) * (x^7 * y^2/x^3) / (16/9)
- Multiply the coefficients: (8 * 1) = 8
- Simplify the powers of x: x^7/x^3 = x^(7-3) = x^4
- Simplify the powers of y: y^2/1 = y^2
- Simplify the denominator: (16/9) = (2/9) * (8/1)
- Multiply the coefficients in the denominator: (2/9) * (8/1) = 16/9
- Simplifying further, we get: 8 * x^4 * y^2 / (16/9)
Final Answer: The simplified expression is 8x^4y^2 / (16/9) or equivalently, (72/16) * x^4 * y^2