Answer:
The equivalent expression for the given expression ![\sqrt[3]{256x^{10}y^{7} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B256x%5E%7B10%7Dy%5E%7B7%7D%20%7D)
is
![4x^{3} y^{2}(\sqrt[3]{4xy} )](https://tex.z-dn.net/?f=4x%5E%7B3%7D%20y%5E%7B2%7D%28%5Csqrt%5B3%5D%7B4xy%7D%20%29)
Step-by-step explanation:
Given:
Solution:
We will see first what is Cube rooting.
![\sqrt[3]{x^{3}} = x](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E%7B3%7D%7D%20%3D%20x)
Law of Indices
Now, applying above property we get
![\sqrt[3]{256x^{10}y^{7} }=\sqrt[3]{(4^{3}\times 4\times (x^{3})^{3}\times x\times (y^{2})^{3}\times y )} \\\\\textrm{Cube Rooting we get}\\\sqrt[3]{256x^{10}y^{7} }= 4\times x^{3}\times y^{2}(\sqrt[3]{4xy}) \\\\\sqrt[3]{256x^{10}y^{7} }= 4x^{3}y^{2}(\sqrt[3]{4xy})](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B256x%5E%7B10%7Dy%5E%7B7%7D%20%7D%3D%5Csqrt%5B3%5D%7B%284%5E%7B3%7D%5Ctimes%204%5Ctimes%20%28x%5E%7B3%7D%29%5E%7B3%7D%5Ctimes%20x%5Ctimes%20%28y%5E%7B2%7D%29%5E%7B3%7D%5Ctimes%20y%20%20%20%29%7D%20%5C%5C%5C%5C%5Ctextrm%7BCube%20Rooting%20we%20get%7D%5C%5C%5Csqrt%5B3%5D%7B256x%5E%7B10%7Dy%5E%7B7%7D%20%7D%3D%204%5Ctimes%20x%5E%7B3%7D%5Ctimes%20y%5E%7B2%7D%28%5Csqrt%5B3%5D%7B4xy%7D%29%20%5C%5C%5C%5C%5Csqrt%5B3%5D%7B256x%5E%7B10%7Dy%5E%7B7%7D%20%7D%3D%204x%5E%7B3%7Dy%5E%7B2%7D%28%5Csqrt%5B3%5D%7B4xy%7D%29)
∴ The equivalent expression for the given expression is
Out of the following choices given, if the liquid drips at the rate of 12 cubic inches per minute, it will take approximately 3.14 minutes for all the liquid to pass through the nozzle. The correct answer will be D.
She buys 24 dvds in 12 weeks.
Answer:
False
Step-by-step explanation:
We have to find the value of x from the given equation.
- (x - 2)(x² - 2x + 2) = 0 is a quadratic equation, so it will have two values.
Step: Write the equation in simplest form.
Step: Solve the problem by spiltting method.
- (x-2)(x² - x -x + 1) = 0
- (x - 2)(x²-x - x + 1) = 0
- (x - 2) [x(x - 1) -1(x -1)]
- (x - 2)[(x-1)(x-1)]
Step: Solve the problem with using algebraic formula.
{x-1](x-1)
Step : We have used a²-b² to solve the problem.
(x-2)(x² - x -x + 1) = 0
(x - 2)(x²-x - x + 1) = 0
(x - 2) [x(x - 1) -1(x -1)]
(x - 2)[(x-1)(x-1)]
Therefore, the possible factorization is (x - 2)[(x-1)(x-1)].
