Simplify the expression. (Do not use mixed numbers in your answer.)
(5x^7/8)(2y^4/6)(x^9/8)(4y^-2/6)
To simplify the expression (5x^7/8)(2y^4/6)(x^9/8)(4y^-2/6), we can follow these steps:
Step 1:
Combine the numerical coefficients. In this case, there are two numerical coefficients, 5 and 2, so their product is 10.
Step 2:
Combine the variables with the same base (x and y) by adding their exponents. For the x variable, we have x^7 and x^9, so their product is x^(7+9) = x^16. For the y variable, we have y^4 and y^-2, so their product is y^(4-2) = y^2.
Step 3:
Combine the fractions by multiplying the numerators and multiplying the denominators separately.
The numerators of the fractions are 5x^7, 2y^4, x^9, and 4y^-2. Their product is: 5x^7 * 2y^4 * x^9 * 4y^-2 = 40x^(7+9) * y^(4+0-2) = 40x^16 * y^2.
The denominators of the fractions are 8, 6, 8, and 6. Their product is: 8 * 6 * 8 * 6 = 2304.
Step 4:
Combine the simplified numerator with the simplified denominator.
The simplified numerator is 40x^16 * y^2, and the simplified denominator is 2304. Therefore, the simplified expression is (40x^16 * y^2)/2304.
So, the simplified expression is (40x^16 * y^2)/2304.