What is the cube root of 192x to the 7th power?
you have ∛(192x)^7
192 = 64*3, so ∛(192x) = 4∛(3x)
(4∛(3x))^7 = 16384 ∛(3x)7
Hmm. I guess we could pull out some 3x stuff to get
16384 (3x)^2 ∛(3x)
= 147456 x2 ∛(3x)
To find the cube root of 192x to the 7th power, we can break down the problem into two steps:
Step 1: Simplify the expression inside the cube root.
The expression inside the cube root is (192x)^7. To simplify this, we can apply the power rule, which states that when raising a power to another power, we multiply the exponents. In this case, we have (192x)^7, so we multiply the exponents 7 and 1 to get 7*1 = 7. Therefore, we can rewrite the expression as (192x)^7 = 192^7 * x^7.
Step 2: Take the cube root of 192^7 * x^7.
To take the cube root, we need to find a number, when raised to the power of 3, will result in 192^7 * x^7. We can split the cube root into two separate roots since the cube root is a multiplicative operation. We can write the expression as the cube root of 192^7 multiplied by the cube root of x^7. So our final expression is:
Cube root of 192^7 * x^7 = Cube root of 192^7 * Cube root of x^7
To calculate the cube root of 192^7, you can use a calculator or mathematical software that has a cube root function. The cube root of x^7 is x^(7/3). So the final answer is:
Cube root of 192^7 * x^7 = Cube root of 192^7 * Cube root of x^7 = Cube root of 192^7 * x^(7/3)
Note: The cube root of a number x can also be represented as x^(1/3). In this case, the cube root of 192^7 can also be written as (192^7)^(1/3).