what is the simplified form of the expression?
(3c^2d^4)^3(2c^5d^8)^3
Use the laws of exponents:
Laws of exponents:
xa * xb = xa+b
xa / xb = xa-b
(xa)b = xab
I'll solve the left part:
(3c^2d^4)^3
=3^3 * (c²)^3 * (d⁴)^3
=27 * c^(2*3) * d^(4*3)
=27 c^6 d^12
To find the simplified form of the expression (3c^2d^4)^3(2c^5d^8)^3, you'll need to apply the properties of exponents and perform the necessary operations step by step. Let's break it down:
First, let's simplify each exponent expression separately:
(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 simplified expressions together:
(27c^6d^12) * (8c^15d^24) = 27 * 8 * c^6 * c^15 * d^12 * d^24 = 216c^21d^36
Therefore, the simplified form of the expression (3c^2d^4)^3(2c^5d^8)^3 is 216c^21d^36.