what is the simplified form of the expression?
(3c^2d^4)^3(2c^5d^8)^3
(3c^2d^4)^3 (2c^5d^8)^3 =
(27c^6d^12) (8c^15d^24=
216c^21d^36.
See:
http://www.jiskha.com/display.cgi?id=1289863704
To find the simplified form of the expression (3c^2d^4)^3(2c^5d^8)^3, we can simplify each exponent separately and then combine the bases and add the exponents.
For the first term, (3c^2d^4)^3, we can use the property of exponents that states (a^b)^c = a^(b*c). Applying this property, we have:
(3c^2d^4)^3 = 3^3 * c^(2*3) * d^(4*3) = 27c^6d^12.
Similarly, for the second term, (2c^5d^8)^3, we have:
(2c^5d^8)^3 = 2^3 * c^(5*3) * d^(8*3) = 8c^15d^24.
Finally, we can multiply the two terms together by multiplying their numerical coefficients and adding their exponents. So, the simplified form of the expression is:
27c^6d^12 * 8c^15d^24 = 216c^21d^36.
To find the simplified form of the expression (3c^2d^4)^3(2c^5d^8)^3, we can use the properties of exponents.
First, let's simplify the terms within each set of parentheses:
(3c^2d^4)^3 = 3^3 * (c^2)^3 * (d^4)^3 = 27c^6d^12
(2c^5d^8)^3 = 2^3 * (c^5)^3 * (d^8)^3 = 8c^15d^24
Next, we'll multiply the expressions together by multiplying the coefficients and adding the exponents of the variables:
27c^6d^12 * 8c^15d^24 = 216c^21d^36
Therefore, the simplified form of the expression (3c^2d^4)^3(2c^5d^8)^3 is 216c^21d^36.