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
However, with the common exponents, the terms could be combined, but still get the same answer:
(3c^2d^4)^3(2c^5d^8)^3 = (3c^2d^4 * 2c^5d^8)^3
To simplify the expression (3c^2d^4)^3(2c^5d^8)^3, we need to apply the power of a power property of exponents. The property states that when raising an exponent to another exponent, you multiply the exponents:
(a^m)^n = a^(m *n)
Let's simplify each term individually first:
(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
Now, we can multiply these two simplified terms together:
27c^6d^12 * 8c^15d^24 = 216c^(6 + 15) * d^(12 + 24) = 216c^21 * d^36
So, the simplified form of the expression (3c^2d^4)^3(2c^5d^8)^3 is 216c^21d^36.