Which expression is another way to write 3 radical 125 x^4?
The expression 3 radical 125 x^4 can be simplified using the fact that 125 is a perfect cube:
3 radical 125 x^4 = 3 radical (5^3) x^4
Then, we can use the rule of exponents that states:
radical (a^b) = a^(b/2)
To obtain:
3 radical (5^3) x^4 = 3(5^(3/2)) x^2
Therefore, another way to write 3 radical 125 x^4 is:
15 radical 5 x^2
To find another way to write the expression 3√(125x^4), we can break it down into smaller parts.
First, let's simplify the radical part of the expression. The cube root (√) of 125 can be written as √(5^3) because 5^3 equals 125. Using the rule of radicals, the cube root of a product is equal to the product of the cube roots. Hence, √(5^3 * x^4) can be simplified as 5√(x^4).
Next, we need to simplify the coefficient in front of the radical. Since the coefficient is 3, we can multiply it by the radical term. Therefore, 3 * 5√(x^4) is equal to 15√(x^4).
So, another way to write the expression 3√(125x^4) is 15√(x^4).