-3x\sqrt[3]{54x^4} + 2\sqrt[3]{16x7}
watch your typing
Is that supposed to be 16x^7 at the end ?
is sqrt[3] supposed to mean "cube root" ?
What is supposed to happen here ?
Are we simplifying ?
If I read your notation right, you have
-3x/√3 54x^4 + 2/√3 16x^7
Seems kind of odd, so maybe it's wrong.
But whatever, is there a question in here somewhere?
Ahh. Maybe you have
-3x∛(54x^4) + 2∛(16x^7)
note that
∛27x^3 = 3x
∛8x^6 = 2x^2
Maybe that will get you started.
To simplify the expression -3x√[3]{54x^4} + 2√[3]{16x^7}, we can simplify the two cube roots separately and then combine like terms.
Let's start by simplifying the first cube root term: -3x√[3]{54x^4}.
Step 1: Simplify the number inside the cube root.
The cube root of 54 can be simplified as √[3]{54} = 3√[3]{2} because 54 can be written as 2 * 27, and 27 is a perfect cube.
Step 2: Simplify the variable part.
The cube root of x^4 can be simplified as √[3]{x^4} = x^(4/3) because we can rewrite x^4 as (x^3)^4.
Putting it all together, the first term becomes -3x * 3√[3]{2} * x^(4/3) = -9x^(7/3)√[3]{2}.
Now let's simplify the second cube root term: 2√[3]{16x^7}.
Step 1: Simplify the number inside the cube root.
The cube root of 16 can be simplified as √[3]{16} = 2√[3]{2} because 16 can be written as 2^4.
Step 2: Simplify the variable part.
The cube root of x^7 can be simplified as √[3]{x^7} = x^(7/3) because we can rewrite x^7 as (x^3)^2 * x.
Putting it all together, the second term becomes 2 * 2√[3]{2} * x^(7/3) = 4x^(7/3)√[3]{2}.
Now that we've simplified both terms, we can combine them: -9x^(7/3)√[3]{2} + 4x^(7/3)√[3]{2}.
Since the two terms have the same radical (√[3]{2}), we can combine them by adding the coefficients (numbers in front of the radical) and keeping the same radical.
Therefore, the simplified expression is: (-9 + 4)x^(7/3)√[3]{2} = -5x^(7/3)√[3]{2}.