Multiply. Assume c is greater than or equal to zero, and write your answer in simplest form.
radical 2c by the power of 3 times 14c by the power of 2
To multiply √(2c)^3 by (14c)^2, we can simplify each expression and then multiply them together.
First, √(2c)^3 simplifies as follows:
√(2c)^3 = (2c)^(3/2)
To raise a power to a power, we multiply the exponents:
(2c)^(3/2) = 2^(3/2) * (c)^(3/2) = 2^(3/2) * c^(3/2)
Next, (14c)^2 simplifies as follows:
(14c)^2 = 14^2 * c^2 = 196 * c^2
Finally, we can multiply the simplified expressions:
(2^(3/2) * c^(3/2)) * (196 * c^2) = 2^(3/2) * c^(3/2) * 196 * c^2
To simplify this expression further, we can combine all the factors with the same base (2 and c) and add their exponents:
2^(3/2) * c^(3/2) * 196 * c^2 = 2^(3/2) * 196 * c^(3/2 + 2)
Now, we can multiply 2^(3/2) * 196 together:
2^(3/2) * 196 = 2^(3/2) * 196 = 274.392
And we can add the exponents for c:
c^(3/2 + 2) = c^(7/2)
Putting it all together, the final simplified expression is:
274.392 * c^(7/2)