the product (2x^4y)(3x^5y^8) is equivalent to?
a.5x^9y^9
b.6x^9y^8
c.6x^9y^9
d.5x^20y^8
e.6x^20y^8
you can immediately rule out a) and d, since 2(3) = 6 not 5
x^4(x^5) = x^9 and y(y^8) = y^9 , so that leaves .... ?
To find the product (2x^4y)(3x^5y^8), you multiply the coefficients and combine the variables with the same base.
The coefficients are 2 and 3, so the product is 2 * 3 = 6.
Next, multiply the variables with the same base:
For the x terms: x^4 * x^5 = x^(4+5) = x^9
For the y terms: y^1 * y^8 = y^(1+8) = y^9
Putting it all together, the product (2x^4y)(3x^5y^8) simplifies to 6x^9y^9.
Therefore, the correct answer is option c. 6x^9y^9.
To find the product of two algebraic expressions, we need to multiply the coefficients and add the exponents of the variables.
In this case, the product is calculated as follows:
(2x^4y)(3x^5y^8) = 2 * 3 * x^4 * x^5 * y * y^8.
Multiplying the coefficients, we get 2 * 3 = 6.
To multiply variables with the same base, we add their exponents. For x, we have x^4 * x^5 = x^(4+5) = x^9.
For y, we have y * y^8 = y^(1+8) = y^9.
Therefore, the product simplifies to:
(2x^4y)(3x^5y^8) = 6x^9y^9.
Therefore, the answer is option c. 6x^9y^9.