cube root of (-64x^8y^5)
Is it -8x^2y times the cube of y^2?
-64 = -4*-4*-4 = -4^3
(x^8)^1/3 = x^(8/3)
(x^5)^(1/3) = x^(5/3
-4 x^(8/3) y^(5/3)
not quite
∛-64 = -4 (8 is √64)
also, you need to divide both exponents by 3. 8=3*2+2 and 5=3+2
so, the answer is
-4x^2y ∛(x^2y^2)
To find the cube root of (-64x^8y^5), we can break it down into two parts - the cube root of -64 and the cube root of (x^8y^5).
1. Cube root of -64:
To find the cube root of a negative number like -64, we first note that it can be expressed as (-4)^3. The cube root of a negative number is equal to the negative of the cube root of its absolute value. Therefore, the cube root of -64 is -4.
2. Cube root of (x^8y^5):
To find the cube root of (x^8y^5), we can individually find the cube root of x^8 and y^5.
- Cube root of x^8:
The cube root of any number raised to a power can be found by dividing the exponent by 3. In this case, the cube root of x^8 is x^(8/3).
- Cube root of y^5:
The cube root of y^5 can be simplified as the cube root of (y^3 * y^2). Using the property of cube roots, we can separate the cube root of a product into a product of cube roots. Therefore, the cube root of y^5 is y * (cube root of y^2).
Combining all the parts, we have:
Cube root of (-64x^8y^5) = -4 * x^(8/3) * y * (cube root of y^2).
Therefore, the answer is not -8x^2y times the cube of y^2, but rather -4 * x^(8/3) * y * (cube root of y^2).