### Prove or disprove that if a and b are rational numbers, then a^b is also rational.

The main objective of this question is to prove or disprove that $a^b$ is a rational number provided that $a$ and $b$ are rational numbers. In

### Find, correct to the nearest degree, the three angles of the triangle with the given vertices. A(1, 0, -1), B(3, -2, 0), C(1, 3, 3).

The main objective of this question is to find the three angles of a triangle given three vertices. The angles can be found using the dot product of

### Find the differential of each function. (a) y=tan (7t), (b) y=3-v^2/3+v^2

The main purpose of this question is to find the differential of each given function. A function is a fundamental mathematical concept that describes

### Determine if the columns of the matrix form a linearly independent set. Justify each answer.

(begin{bmatrix}1&4&-3&0\-2&-7&4&1\-4&-5&7&5end{bmatrix}) The main objective of this question is to determine

### Solve the equation explicitly for y and differentiate to get y’ in terms of x.

(dfrac{1}{x}+dfrac{1}{y}=1). The main objective of this question is to explicitly write the given function in terms of $x$ and to express $y’$