Question

Simplify completely, assuming both x > 0 and y > 0: 9x^3y^6√ a) 3x^2y^3 b) 3x^3y^6 c) 27x^2y^3 d) 27x^3y^6

Answer 1

The expression 9x^3y^6√ simplifies to 9x^2y^3 by using the principle of cubing exponentials, which does not match with the provided options. Hence, none of the options are correct.

Step-by-step explanation:

The given expression is

9x^3y^6√

. To simplify this expression completely, we need to use the principle of

cubing exponentials

. In this principle, we cube the digit term in the usual way and multiply the exponent of the exponential term by 3. This gives: 3√(9x^3y^6) = 3* 3x^2y^3, as the cube root of each term in the parentheses is calculated separately. So, cube root of 9 gives 3, of x^3 gives x and of y^6 gives y^2. Then we multiply all these results by 3. Thus, the simplified form of the given expression is

9x^2y^3

, which does not match with any of the provided options. Hence, none of the options a), b), c), d) are correct.

Learn more about Simplifying Exponential Expression